Article

# The Theory of Moral Hazard and Unobservable Behaviour: Part I

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## Abstract

Principal-agent models are studied, in which outcomes conditional on the agent's action are uncertain, and the agent's behaviour therefore unobservable. For a model with bounded agent's utility, conditions are given under which the first-best equilibrium can be approximated arbitrarily closely by contracts relating payment to observable outcomes. For general models, it is shown that the solution may not always be obtained by using the agent's first-order conditions as constraint. General conditions of Lagrangean type are given for problems in which contracts are finite-dimensional.

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... BLPPs have broad applications. For example, they appear in the principal-agent moral hazard problem [34] and electricity markets and networks [5]. Recently, BLPP has been applied to hyperparameter optimization and metalearning in machine learning; see, e.g., [29,18,30,51]. ...
... When there are no upper-and lower-level constraints in BLPPs, our result (Corollary 6.5) shows that the condition in [54, Theorem 2.1] is a generic one. This gives a rigorous proof of Mirrlees's arguments about f -critical points in [34]. ...
... \bullet The classic principal-agent moral hazard problem In the situation of the moral hazard principal-agent problem, the agent chooses an action a \in A that is unobservable to a principal. The action a influences the random outcome s \in S through a parameterized probability measure P (\cdot | a) (see [34]). The outcome s leads to a monetary payoff \pi (s), which accrues directly to the principal. ...
... Une simplification alors possible pour obtenir une première intuition sur le comportement des contrats dans un nouveau cadre consiste à enlever la notion du temps continu et de se restreindre à des modèles "jouets" discrets. Si cela peut enlever un niveau de complexité, il faut tout de même faire attention : il existe un célèbre résultat de non-existence dans un cadre discret, formulé par Mirrlees dans [101] en 1999 que nous allons présenter. Pour cela, introduisons un équivalent à une seule période du problème de Moral Hazard présenté ci-dessus et discuté dans [37]. ...
... Reverse-Hölder apply for Moral Hazard, we would expect similar unification yet Mirrlees' has proven non-existence for optimal contracts in the single period Moral Hazard problem (see [101]). In fact, as mentioned in Chapter 1 solving the Moral Hazard problem in a single period problem is often simply not possible for arbitrary contracts... ...
... C'est pour ce problème que Mirrlees a exhibé dans[101] une non-existence de contrats optimaux. Plus particulièrement, il n'existe pas de contrat(W ú , a ú ) résolvant (1.2.1)-(1.2.2)-(1.2.3),et c'est en fait le problème de l'Agent (1.2.1) qui pose problème. ...
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Thesis
In this thesis, we analyse several incentive problems under societal constraints. To this end we use the Principal-Agent formalism and base ourselves on the founding model of Hölmstrom and Milgrom. We first look at full information problems in this model and establish a alternative and unifying framework their resolution with broad application. As well as shining a new light on the meaning of the Borch rule in economy, this approach extends the interpretation of the Agent’s optimal action. This method is then applied in the full information part of a first incentive problem where we analyze the effet of task-based pay, characterizing contracts in the gig economy. The Principal’s wealth is modeled through a Poisson process of which the Agent can change the intensity. The optimal contracts are explicit, with a slight modification of the classical linearity expected under partial information in this model. We note that despite the Principal’s positive wealth, the Agent’s wage can be negative which underlines the stakes related to adding positivity constraints to such problems. We therefore then turn to such constrained incentive problems in a discrete model. We establish solution existence through a variational approach under relatively general utilities. These solutions are then characterized through first order methods, allowing some analysis of the effect of constraints on contracts. In particular, we obtain optional type wages. Finally, we turn to a problem related to current affairs : incentives under a risk of economic shutdown. To do so, we extend the Hölmstrom-Milgrom model by adding a default process and we obtain an explicit wage that is linear in the default time. This model is then extended to included a possibility of continued activity despite the shutdown, conditioned on sufficient investment from the Principal. We conclude this thesis with the proof of a necessary result for this last incentive problem : existence and uniqueness of solutions to a certain Brownian backward stochastic differential equation with default.
... BLPPs have broad applications. For example, they appear in the principal-agent moral hazard problem [34], electricity markets and networks [5]. Recently, BLPP has been applied to hyperparameters optimization and and meta-learning in machine learning; see e.g. ...
... When there is no upper and lower level constraints in BLPPs, our result (Corollary 6.5) shows that the condition in [54, Theorem 2.1] is a generic one. This gives a rigorous proof of Mirrlees' arguments about f -critical points in [34]. ...
... • The classic principal-agent moral hazard problem In the situation of the moral hazard principal-agent problem, the agent chooses an action a ∈ A that is unobservable to a principal. The action a influences the random outcome s ∈ S through a parameterized probability measure P (·|a) (see [34]). The outcome s leads to a monetary payoff π(s), which accrues directly to the principal. ...
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Preprint
The partial calmness for the bilevel programming problem (BLPP) is an important condition which ensures that a local optimal solution of BLPP is a local optimal solution of a partially penalized problem where the lower level optimality constraint is moved to the objective function and hence a weaker constraint qualification can be applied. In this paper we propose a sufficient condition in the form of a partial error bound condition which guarantees the partial calmness condition. We analyse the partial calmness for the combined program based on the Bouligand (B-) and the Fritz John (FJ) stationary conditions from a generic point of view. Our main result states that the partial error bound condition for the combined programs based on B and FJ conditions are generic for an important setting with applications in economics and hence the partial calmness for the combined program is not a particularly stringent assumption. Moreover we derive optimality conditions for the combined program for the generic case without any extra constraint qualifications and show the exact equivalence between our optimality condition and the one by Jongen and Shikhman given in implicit form. Our arguments are based on Jongen, Jonker and Twilt's generic (five type) classification of the so-called generalized critical points for one-dimensional parametric optimization problems and Jongen and Shikhman's generic local reductions of BLPPs.
... Also note that our model formulation implicitly assumes that the agent cannot operate a private account for him/herself so that he/she cannot unwind the incentive scheme. 14 An example by Mirrlees [24] shows that the first-order condition is not sufficient for global optimum, and as a result, the first-order approach can no longer be applied. 15 These assumptions are not crucial in solving the contracting problems but rather for convenience. ...
... Proposition 4 Given a set of (λ, λ , λ w , λ v ) and an initial condition (x( ) = λ , x ( )) that satisfies constraint (24), the ODE (23) has a unique solution that satisfies constraint (24). ...
... Proposition 4 Given a set of (λ, λ , λ w , λ v ) and an initial condition (x( ) = λ , x ( )) that satisfies constraint (24), the ODE (23) has a unique solution that satisfies constraint (24). ...
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Article
The optimal contracts in portfolio delegation under general preferences are characterized when the underlying state variable is not contractible, and the principal must rely on the final returns of portfolios to design the compensation schemes for the fund manager. We show that the optimal contracts satisfy a second-order nonlinear ordinary differential equation that depends on the utility functions and the distribution of state price density. In general, there is an efficiency loss for the optimal contracts unless the utility functions of both the principal and the agent exhibit linear risk tolerance with identical cautiousness. Additional contractible observables, like stock indexes, can be used to improve the efficiency of the second-best contracts, even if they are not perfectly correlated with the underlying state price. A continuous-time example with power utilities is presented to illustrate the features of the optimal contracts.
... In a well-known example, Mirrlees (1999) shows that a solution to the agency problem may not exist and that a sequence of step contracts can arbitrarily approach the first best contract. Hölmstrom (1979) offers an in-depth explanation of Mirrlees' type of asymptotic first best in terms of the economics of information and argued that if the log likelihood ratio is unbounded (either from below or above), then the signals generated by the agent's action become rich enough to deliver sufficient information about such action. ...
... First, the approximating sequence does not converge at all due to the complexity of the infinite dimensionality of the contract space. Second, even if a certain approximating contract sequence has a limit, such limit may fail to implement the desired action as in the counter example ofMirrlees (1999). 2 These new findings provide an affirmative answer to Hölmstrom's conjecture. ...
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Article
This paper proposes a new method for investigating the existence of a deterministic solution to pure moral hazard problems under a general setting without imposing a priori topological restriction on the contract space. Our method avoids the detour to show the existence of a random contract before showing the existence of a deterministic contract. We show the existence of a solution in the classical moral hazard setting wherein the agent’s utility is separable between money and effort, and the utilities of the principal and agent are concave in money. The proposed sufficient condition for the existence is comparable with the state-of-the-art results, and we use an easy-to-check approach. For example, we show the existence if the marginal incentive cost (per util given to the agent) is unbounded, or if the signal is finite. Also our approach can apply to multi-agent settings and the cases in which the agent utility is quasi-separable.
... Bilevel programs are a class of hierarchical optimization problems which have constraints containing a lower-level optimization problem parameterized by upper-level variables. Bilevel programs capture a wide range of important applications in various fields including Stackelberg games and moral hazard problems in economics ( [29,41]), hyperparameter selection and meta learning in machine learning ( [16, 21-23, 26, 27, 30, 31, 34]). More applications can be found in the monographs [3,12,15,40], the survey on bilevel optimization [11,14] and the references within. ...
... We now assume that the lower level objective f is differentiable and ∇ f is Lipschitz continuous with modulus L f on set C. Given a current iterate (x k , y k ), the next iterate (x k+1 , y k+1 ) can be returned as an approximate minimizer of subproblem (29) with linearized f given by ...
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Article
In this paper, we present difference of convex algorithms for solving bilevel programs in which the upper level objective functions are difference of convex functions, and the lower level programs are fully convex. This nontrivial class of bilevel programs provides a powerful modelling framework for dealing with applications arising from hyperparameter selection in machine learning. Thanks to the full convexity of the lower level program, the value function of the lower level program turns out to be convex and hence the bilevel program can be reformulated as a difference of convex bilevel program. We propose two algorithms for solving the reformulated difference of convex program and show their convergence to stationary points under very mild assumptions. Finally we conduct numerical experiments to a bilevel model of support vector machine classification.
... It is known that when the lower level problem is nonconvex, the KKT reformulation has a larger feasible set than the bilevel program, and thus the bilevel program and the MPCC are not equivalent [88]. On the other hand, it was believed for a long time that if the lower level problem is convex then the two problems are equivalent. ...
... For problem Mirrlees1999, all algorithms found the solution point x = 1.99, y = 0.895. This was stated in the paper by Mirrlees[88] as a solution to the KKT reformulation that is not a solution to the bilevel problem. The problem with this solution is that y = 0.895 is a local minimum of the lower level problem for x = 1.99, and is not the global minimum. ...
Thesis
A bilevel optimisation problem is an optimisation problem which has a second optimisation problem embedded in its constraints. It aims to model problems and decision processes that are hierarchical, which are problem structures that occur frequently in real-life. Thus, due to the wide range of applications of bilevel problems, there is a strong motivation to solve them. The aim of this thesis is to develop an approach to solving bilevel programs by utilising the less commonly used optimal value reformulation. The work can be split into two main contributions. First, a novel trust-region approach to solving nonlinear bilevel problems is proposed, which solves an exact penalisation of the optimal value reformulation. Second, an application of bilevel programming to the London congestion pricing problem is explored, investigating the application of the proposed trust-region method to solve a bilevel formulation of the road pricing problem. One of the most common approaches to solving a bilevel program is to first transform the problem into a single level program. The most popular way of doing so is by replacing the lower level problem by its Karush-Kuhn Tucker conditions. That being said, the reformulation requires strong assumptions on the bilevel program for it to be equivalent to the original problem. An alternative method to transform the problem into a single level problem is to use the optimal value function of the lower level problem. This problem is known to be fully equivalent. However, due to the difficulties in solving it, approaches in the literature that utilise this reformulation are relatively scarce. Under a regularity condition known as the partial calmness condition, an exact penalty problem can be built from the optimal value reformulation. The first contribution of this thesis is the investigation of solving this exact penalty problem to find local solutions of the associated bilevel problem. A novel trust-region algorithm is proposed to solve it, and convergence analysis is explored. The implementation and performance of the algorithm is investigated via extensive numerical experiments on a large test set of nonlinear bilevel problems. This provides strong numerical results that validate the approach for solving bilevel problems. Based on the results and analysis, the performance and limitations of the algorithms are discussed. The second contribution of this thesis is exploring the application of the aforementioned trust-region method on the bilevel optimisation formulation of the road pricing problem. Road pricing is a method used by governments to alleviate congestion in an overcrowded network. The problem has a hierarchical structure, and therefore naturally forms as a bilevel program. We investigate a case study of the problem to the London congestion zone charge: a fixed cordon road pricing scheme implemented in the center of London. Although successful on initial implementation in 2003, congestion in the city has returned to pre-charge levels. Due to recent advances in technology, the Mayor of London is looking to update the congestion charge to a more sophisticated tolling scheme that can charge for distance, time, emissions or other factors. A formulation of the London congestion problem as a bilevel program is presented, which considers the aims and objectives set out by the current Mayor of London. We then show how the trust-region algorithm can be applied to solve a simplified form of the road pricing model commonly seen in the literature. This is a novel approach to the problem, solving a single level continuous exact penalty problem to find local solutions of the road pricing bilevel model. The performance of the algorithm is tested and verified numerically on three network examples of varying sizes, and the efficiency and robustness of the algorithm is assessed.
... We derive this result by construction: a principal can always write a contract so that the resulting concavifying hyperplane of the agent's payoff function is tangent to the payoff from taking the outside option at the prior. Importantly, this is not a "shoot the agent contract" (Mirrlees (1999))-the principal can attain (not approximate) the first best even if the agent's utility function is bounded. In fact, as long as the agent's outside option is sufficiently high, efficient implementation is feasible even when negative transfers are forbidden. ...
... Finally, because we study the motivation of an agent to acquire costly and unverifiable information, our work also connects to the moral hazard literature. In the canonical moral hazard problem (see, for example, Mirrlees (1999), Holmström (1979), and Grossman and Hart (1983)), the agent is impelled to exert costly effort that yields some output; whereas in ours, she must be coerced into choosing a much more complicated object (a particular probability distribution) then reporting honestly. That being said, there are some interesting analogies between some of our results and classical insights in the moral hazard problem, which we discuss as we encounter them. ...
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Preprint
A principal hires an agent to acquire a distribution over unverifiable posteriors before reporting to the principal, who can contract on the realized state. An agent's optimal learning and truthful disclosure completely specify the marginal incentives the principal must provide, which radically simplifies the principal's problem. When the agent i. is risk neutral, and iia. has a sufficiently high outside option, or iib. can face sufficiently large penalties, the principal can attain the first-best outcome. We also explore in detail the general problem of cheaply implementing distributions over posteriors with limited liability constraints and a risk-averse agent.
... The term "moral hazard problem", by extension, has been applied to the principal agent problem (Stiglitz 1989). Mirrlees (1999), Holmström (1979), and Grossman and Hart (1983) have made key contributions to this area. They found that, once the contract has been signed, the agent takes advantage of hidden action and hidden information and can take more risks, because the principal bears the cost of the risks. ...
... They found that, once the contract has been signed, the agent takes advantage of hidden action and hidden information and can take more risks, because the principal bears the cost of the risks. For example, once a car insurance contract is signed, the insurance company (the principal) observes whether or not the driver is careful enough, and the driver (the agent) might not drive carefully because the insurance company bears the cost of the accident (Mirrlees 1999). A moral hazard also affects securitization market risks once the information asymmetry between lenders and securitization issuers (SPV) increases. ...
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Article
E-commerce and FinTech are currently booming in China. The growing consumer market is accompanied by internet finance, by which consumers can easily borrow money from financial institutions online. As a result, the growing risks of financial institutions are of concern to the government and regulatory bodies. Consequently, the securitization market in China is seeing rapid growth that could affect financial stability. Applying FinTech and emerging technologies in securitization might be an effective way to protect against these risks. This paper studies the question of whether China needs a higher standard of information transparency in order to protect against its risks against the background of digital transformation. We analyzed the determinants of securitization in the Chinese banking sector, relying on data on banks for two periods: pre-2017Q4 and post-2017Q4. The main findings of the paper demonstrate that the application of FinTech in China’s banking industry resulted in less information asymmetry. The risk exposure was the most significant determinant in general. Higher risk exposures increased securitization transaction volumes, which reflects securitization with adverse selection problems between the originator and investors. Liquidity and profitability, as important determinants indicating the moral hazard problem, also affected securitization pre-2017Q4, but liquidity and profitability were found to be unimportant determinants after the application of FinTech (the post-2017Q4 period). Moreover, this study finds that the effects of the adverse selection and moral hazard problems varied in different types of banks. Overall, our findings suggest that the Chinese securitization market needs a higher standard of information transparency.
... As opposed to the previous case, in which agents were offered a menu of contracts, moral hazard situations imply that every agent is given the same contract; the contract must therefore take into account future information asymmetries and hence address the incentives problem. Mirrless (1999), Holmstrom (1979, and (Grossman and Hart, 1983) were key contributors to this literature. To illustrate this phenomenon, Mirrless (1999), car insurance market model would be considered: a driverthe agent wants to buy insurance from an insurance companythe principal. ...
... Mirrless (1999), Holmstrom (1979, and (Grossman and Hart, 1983) were key contributors to this literature. To illustrate this phenomenon, Mirrless (1999), car insurance market model would be considered: a driverthe agent wants to buy insurance from an insurance companythe principal. The source of concern is that once the insurance contract is signed, the insurance company cannot observe whether the driver is careful enough. ...
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Article
This research survey examines the consequence of unbalanced information in the Kano used phones markets. The study also examines the degree to which prices convey information on product quality to uninformed party. Information asymmetry deteriorates the existence of market selling good quality products because the unbalanced information rendered to the buyers during their purchase provokes them to acquire the ownership of it. Incentives were obtainable by the sellers to sell these poor quality products which were also the reason that drive away the good quality businesses from the markets. To properly examine the effects of asymmetric information in the Kano used phones markets, the research administered questionnaire to 50 respondents and conducted interview with 6 respondents, comprising 3 sellers and 3 buyers. The findings of the study suggest that there is a relationship between differences in information available to the market participants and dishonesty rate on the part of the sellers. It revealed that the introduction of warranty, to encourage sales, created incentive for dishonest behavior on the part of the buyers. Hence the presence of moral hazard in the market is reaffirmed. The research further found that the above stated problems are reinforced by the lack of a formal regulatory agency in the markets. Finally, this study recommended the following: the establishment of a formal regulatory agency, registration of sellers with corporate affairs commission (CAC) and the continuous usage of brand names and warranty among others.
... Contrary to the case of adverse selection where a menu of contracts are offered to agent, moral hazard situations implies that every agent is given the same contract; the contract must therefore take into account future information asymmetries, and hence address the incentives problem. Mirrlees (1999) [12] , Holmström (1979) [5] and Grossman and Hart (1983) [9] were key contributions to this literature. Moral hazards in the financial markets usually featured through the inability of managers of companies as agents of shareholders to maximize the wealth of these individuals. ...
... Contrary to the case of adverse selection where a menu of contracts are offered to agent, moral hazard situations implies that every agent is given the same contract; the contract must therefore take into account future information asymmetries, and hence address the incentives problem. Mirrlees (1999) [12] , Holmström (1979) [5] and Grossman and Hart (1983) [9] were key contributions to this literature. Moral hazards in the financial markets usually featured through the inability of managers of companies as agents of shareholders to maximize the wealth of these individuals. ...
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Article
This study examined the effect of cash flow on banks' lending to SMEs in Nigeria. Although, cash flow lending is getting recognition nowadays, little is known about its impact on banks' lending to SMEs particularly in Nigeria. Studies in the past dwelled much on the assessment of government programmes to support the creation of SMEs, but grossly overlooked the analytical impact of such policies on efficient allocation of credit to SMEs. As an attempt to fill this gap, this study answered the following questions; what factors determine cash flow lending to SMEs in Nigeria? To answer the question we used a data consisting of 49 non-financial firms listed in the Nigerian stock exchange for the period 2005 to 2018 and employed both pooled and random effect estimation techniques. The result from the study shows that both current and previous cash flow positively and significantly affect the amount of credit granted to firms by the banks. Additionally, deterioration of firms' net situations reduces the amount of credit granted by banks to firms. The study thus, recommends that Government should remove all unnecessary bureaucratic hurdles and discrimination, establish strategic and robust venture capital sector, crowd funding and other forms of financial institutions such as micro finance institutions to make funds available at affordable rate to critical sectors such as agriculture and manufacturing.
... Every insurance contract possesses some degree of moral hazard and its effects are sometimes hard to detect even though anecdotal evidence of the importance of moral hazard is widespread (Haldane & Kruger, 2001). It is already clear that the case of moral hazard in insurance is a very general one, arising whenever behavior is unobservable, but its consequences are observable (Mirrlees, 1999). Just to give some examples of this kind of behavior, not arising from the insurance world, it is possible to think of the possibility that individual traders will take actions, specifically, excessive risk-taking, at the expense of the firm as a whole, the possibility that bank management will not act in the shareholders' interests or the recurrent problem of excessive risk-taking in bank loan portfolios, that is often a moral hazard problem (Dow, 2000). ...
... An example of solutions found in the insurance industry to reduce moral hazard is to link payments in a proportional way to expenditures, with individuals choosing their expenditures to suit themselves. In this sense lending limitations or constraints can help to reduce the phenomenon (Haldane & Kruger, 2001;Mirrlees, 1999). Another possible direction for the resolution of the phenomenon is monitoring the actions and using this information to draw up contracts. ...
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Article
During economic crises, sovereign states and central banks support the general economy and firms with a range of emergency measures, such as the allocation of subsidies to enterprises and citizens. The sudden availability of money without the need for any consideration by the recipient leads the way to inappropriate conduct known as moral hazards, such as diversion or improper use of the financial resources received. The moral hazard arises from the individual tendency to rational behavior when in the presence of information asymmetry, inadequate controls, or favorable contractual positions. To reduce moral hazard, and to preserve the intentionality of the states, information asymmetry must be reduced. Avoiding moral hazard is particularly important in cases such as the COVID-19 pandemic, but also during economic crises and other emergency situations. This paper conceptualizes a relevant topic for the economy and accounting fields of study because information tends to be naturally asymmetrical. Traditional accounting is limited by the fact that some accounting practices or techniques can be used to reduce the effect of the pandemics on the economic performance of organizations. In our study we propose a way to reduce the natural subjectivity in accounting and reporting, using blockchain and smart contracts technologies, as a solution to information asymmetry during crises (such as economic ones or pandemics)
... Vickrey's conclusions on market asymmetry were further developed and summarised by a Nobel Laureate, sir James Mirrlees. He significantly expanded the set of economic problems characterised by information asymmetry by proposing many mathematical models for their resolution (Mirrlees, 1974(Mirrlees, , 1999. ...
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Article
Aim. The article aims to analyse the manifestations of information asymmetry in the market of educational services to develop proposals for improving the communication programmes of higher education institutions of Ukraine. Methods. The authors describe the display of information asymmetry in the market of educational services based on a sociological study among the 1st and 2nd-year students of Ukrainian universities, which aimed to study the criteria for choosing an educational programme. The authors used correlation analysis to assess the statistical significance of the influence of individual criteria on the selection of entrants. The survey was conducted at the universities in Ukraine that provide educational services on the bachelor’s degree specialities of 073 Management and 075 Marketing. A critical and comparative analysis of state regulatory measures to overcome information asymmetry was also applied. Results. The annual decrease in the number of university entrants in Ukraine and around the world has led to increased competition among universities, resulting in an escalation of information asymmetry in the market of educational services and its ‘lemonisation’. Conclusions. According to the results of the sociological study, despite the high availability of sources of information, at the time of entering the university, the vast majority of students did not consider themselves sufficiently informed about the benefits of studying in the chosen educational and professional programme. Several state regulatory measures have been taken to provide quality educational services in Ukraine and ensure unbiased information about universities. It was revealed that by allocating state-funded places for a specific speciality and university, the government significantly influences the choice of applicants. However, it should be noted that such impact is not very significant for applicants with high scores. Given this, the impact and effectiveness of both the state regulation system of universities in Ukraine and its specific instruments require further study. Cognitive value. The study results contribute to overcoming the asymmetry of information in the market of educational services, serve as a methodological basis for improving the communication programmes of higher education institutions, promote healthy competition among them. The findings of this study can be considered an essential contribution to future research.
... In addition, since the insurer incurs significant administrative overhead, broker commissions, and premium taxes, it is not efficient to insure small or frequent losses. The retention eliminates these costs because the insured pays small claims directly (e.g., Grossman and Hart 1983;Holmstrom 1979;Mirrlees 1999). The policy period begins at the acquisition's closing and ends at an agreed upon expiration date. ...
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Article
To mitigate information asymmetry in acquisitions, the seller makes contractual representations and warranties (referred to as “R&W” or “reps”) about the state of the target, such as attesting to the accuracy of the target’s financial statements. While seller indemnities allow buyers to impose costs due to breaches in the reps discovered after the deal’s close, these indemnities involve significant contracting costs. To mitigate these costs, the acquisition parties have increasingly turned to purchasing representations and warranties insurance. Using a proprietary and novel sample of R&W insurance policies issued worldwide for acquisitions of non-public targets, we find that the demand for R&W insurance, the premium charged for it, and the likelihood of a claim being filed are correlated with industry metrics for valuation uncertainty, the type of acquirer and seller, and the target’s legal regime. In particular, we find higher demand for R&W insurance and a higher R&W insurance premium charged when the target belongs to an industry with weaker internal controls. We also find that a higher premium is charged when the target is in an industry with relatively high levels of R&D to sales, indicating that the insurance company expects unrecognized intangible assets to have a greater risk of future claims. Our study adds to our understanding of how parties reduce target valuation uncertainty and the role of disclosures and R&W insurance policies in private mergers and acquisitions transactions.
... The Principal-Agent problem was originally introduced in the 1970s and studied among others by Mirrlees [29;30], Hölmstrom [22], Shavell [40], Grossman and Hart [20], Rogerson [37] and Jewitt [28]. In the last decade it has regained part of the importance it had in financial mathematics, mainly since the seminal paper by Sannikov [39] which proposed a new approach for the continuous-time version of the problem, that had been proposed long ago by Holmström and Milgrom [24]. ...
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We study a general contracting problem between the principal and a finite set of competitive agents, who perform equivalent changes of measure by controlling the drift of the output process and the compensator of its associated jump measure. In this setting, we generalize the dynamic programming approach developed by Cvitani\'c, Possama\"i, and Touzi [12] and we also relax their assumptions. We prove that the problem of the principal can be reformulated as a standard stochastic control problem in which she controls the continuation utility (or certainty equivalent) processes of the agents. Our assumptions and conditions on the admissible contracts are minimal to make our approach work. We review part of the literature and give examples on how they are usually satisfied. We also present a smoothness result for the value function of a risk-neutral principal when the agents have exponential utility functions. This leads, under some additional assumptions, to the existence of an optimal contract.
... Then replace the complementarity constraints with some linearization techniques, e.g., the big-M method, to yield a mixed-integer linear programming model, which is finally solved with commercial solvers. However, this method is only possible if the lower-level problem is convex [49]. As the equality constraint (31) is not affine, model L is nonconvex [50]. ...
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Article
Uncertainties from neighboring rival’s reservoirs challenge hydropower companies in participating in competitive markets. Cooperative behaviors are generally impractical due to stakeholders’ self-interest and regulatory requirements. Considering this obstacle, this paper proposes a data-driven bilevel model, in a competitive context, to estimate the operational information of the neighboring rival’s reservoir, including its historical operating states and operational functions. The proposed bilevel model is an inverse problem of the conventional hydropower scheduling model. The upper-level model is designed to find the most appropriate operational parameters of the estimated reservoir that fit its historical generation volumes. The lower-level model simulates the profit-maxing operation of the estimated reservoir. Since the lower simulating model is nonconvex, an Enhanced Parallel Genetic Algorithm (EPGA) is proposed. It avoids infeasible situations through several strategies and uses multiple CPU threads simultaneously in solving. A case study in China’s market demonstrates that the proposed model and solving method can efficiently obtain accurate state series and (near-)optimal operational parameters. More experiments are also taken to validate the parallel design.
... This is equivalent to the average test score in our setup, given a monotonic relationship between effort and scores. 4 This positive emphasis contrasts with the normative approach in the optimal contracting literature; seeMirrlees (1975) and related theoretical studies. Implementing the optimal contract would raise feasibility issues beyond the scope of the current analysis. ...
... One lesson from agency theory (Holmstrom, 1979;Mirrlees, 1999) is that the optimal contract between the Principal (pursuing some collective goal) and the Agent (making in-field decisions) involves trading off incentives and risk-sharing with robust financial institutions. Since public budgets are risk bearers of the last-resort, risk-sharing mechanisms for LCIs must both cover the projects' early phases and maximize the efficacy of any public funding spent. ...
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Article
In this paper, we examine how to trigger a wave of low-carbon investments compatible with the well-below 2°C target of the Paris Agreement in the current post-pandemic context of increasing private and public debt. We argue that one major obstacle to catalysing global excess savings at sufficient scale and speed on climate mitigation, and to ‘greening’ economic recovery packages, lies in the up-front risks of low-carbon investment. We then explain why public guarantees should be the preferred risk-sharing instrument to overcome that obstacle. We outline the basic principles of a multilateral sovereign guarantee mechanism able to maximize the leverage effect of public funds and massively redirect global savings towards low-carbon investments, with the double benefit of bridging the infrastructure investment gap in developing countries and reducing tension between developed and developing countries around accelerated funding for low-carbon transitions. We carry out numerical simulations demonstrating how the use of guarantees from AAA-rated sovereigns, calibrated on an agreed-upon ‘social value of carbon’, is compatible with public-budget constraints of developed countries. In summary, the use of such guarantee mechanisms provides a new form of ‘where flexibility’, which could turn real-world heterogeneity into a source of reciprocal gains for both developed and developing countries, and contribute to meeting the USD 100 billion + pledge of the Paris Agreement. Key Policy Insights • Catalysing excess world savings through low-carbon investments (LCIs) would secure a safer and fairer economic recovery from the COVID-19 crisis and avoid locking developing countries into carbon-intensive pathways. • Public policy instruments focused on the creation of public guarantees can reduce the up-front financial risks associated with LCIs, mobilize private money and increase the leverage of public finance. • A multi-sovereign guarantee mechanism would yield financial support from developed to developing countries in cash grant equivalent and equity inflows two to four times higher than the ‘USD 100 billion and more’ commitment of the Paris Agreement, and provide greater confidence in meeting this commitment equitably and effectively with benefits for all.
... Companies want to motivate purchasing agents to seek cost saving and better value for the organization (Nollett et al. 2008;Pohl and Foerstl 2011). These organizations also want to safeguard the legitimacy of real cost saving that contribute to the organization's success, while preventing the moral hazard of giving credit for savings, when credit isn't due (Mirrlees 1976(Mirrlees , 1999Nollett et al. 2008;Tchokogu e et al., 2017). In sum, cost saving are desirable; defining them can be murky. ...
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Book
... Unless otherwise specified, we assume that F, G, f, g are continuously differentiable and f, g are three times continuously differentiable. The bilevel programming problem has many applications including the principalagent moral hazard problem [28], hyperparameters optimization and meta-learning in machine learning [23,17,25,40]. More applications can be found in [32,3,10,11]. ...
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Preprint
In this paper, we propose a combined approach with second-order optimality conditions of the lower level problem to study constraint qualifications and optimality conditions for bilevel programming problems. The new method is inspired by the combined approach developed by Ye and Zhu in 2010, where the authors combined the classical first-order and the value function approaches to derive new necessary optimality conditions under weaker conditions. In our approach, we add the second-order optimality condition to the combined program as a new constraint. We show that when all known approaches fail, adding the second-order optimality condition as a constraint makes the corresponding partial calmness condition easier to hold. We also give some discussions on optimality conditions and advantages and disadvantages of the combined approaches with the first-order and the second-order information.
... For more information on moral hazard, see Davies and Kuhn (1992) and Mirrlees (1999). ...
Article
Although international remittances are expected to spawn welfares within the recipient economies, the public moral hazard problems associated with such inflows often trigger apprehensions. Against this backdrop, this paper aimed to evaluate the public spending responses to inward foreign remittances in Bangladesh. The results confirm that higher volumes of remittances reduce the overall level of public spending as well as public health expenditure in Bangladesh. In contrast, incoming remittances are found to persistently enhance public expenditure in the education sector. Moreover, rising income inequality, deteriorating democratic practices and poor governance in Bangladesh are found to aggravate the public moral hazard problems associated with the influx of international remittances.
... Furthermore, recent literature has suggested that loss aversion is lower in settings where individuals make decisions for others rather than themselves (Polman, 2012;Mengarelli et al., 2014;Zhang et al., 2017). The finding can be theoretically linked to the principal-agent model in economic theory (Ross, 1973;Stiglitz, 1974;Mirrlees, 1999), where an agent is assumed to be less responsible in making choices for her principal than for herself due to conflicted objectives (i.e., when there is inconsistency between maximising her principal's benefit and the benefit of herself). In that case, the agent would be less sensitive to the losses of others than those for herself (Mengarelli et al., 2014). ...
Thesis
Outdoor air pollution is one of the most detrimental issues to human health, and has triggered massive concern in many cities globally. Due to the public nature of the good, negative externalities caused by air pollution from industrial and individual activities cannot be solved by the market, and the central government has to step in to reduce air pollution. However, governments in developing countries are not always fully incentivised to combat pollution due to concern about reduced economic growth, and governmental action depends on the trade-off between air quality and economic development. To inform this trade-off decision, estimates for both the benefits of air quality improvement and the costs of air quality deterioration are required. This thesis aims to elicit individuals’ preferences for air quality changes using discrete choice experiments. The study area is Beijing, China, where severe air pollution has existed over the last decade. The experimental design involves hypothetical policy scenarios that describe changes in the health and visibility aspects of air pollution, and changes in policy cost (i.e., household energy bills). The first issue I investigate in the thesis is whether losses from air quality deterioration are larger than gains from air quality improvement. Using a unique gain-loss experimental design that allows to measure utility gains and losses simultaneously, this thesis finds that people place more weight on air quality losses than gains. I also find that social capital plays a role in individuals’ preferences for air quality changes, and that it correlates with loss aversion preferences. Additionally, the findings provide evidence of non-compensatory behaviour and unwillingness to trade reduction of air quality for monetary compensation. Environmental outcomes are often affected by the stochastic nature of the environment and ecosystem, as well as the effectiveness of governmental policy in combination with human activities. The second issue explored in this thesis is whether, and how, individuals incorporate uncertainty around policy outcomes in their decision making. Using a discrete choice experiment where the risk of outcome delivery is included in the design as an additional attribute, I find that respondents’ utility decreases when risk increases. However, people treat risk as if it is independent of its related policy outcomes in scenarios of both air quality gain and loss. Following the investigation of how risk is taken into consideration in a discrete choice experiment, the third topic investigated is whether people’s environmental preferences are affected by the effects of risky choice framing. In a new experimental design, where policy is described as risky, the expected outcomes of the policy are set to be equal to those in a certain treatment where outcomes are riskless. The information of expected outcomes is embedded in the attribute to assist decision making. The results suggest that risky framing in policy scenarios has little effect on people’s air quality preferences.<br/
... Bilevel programs are a class of hierarchical optimization problems which have constraints containing a lower-level optimization problem parameterized by upper-level variables. Bilevel programs capture a wide range of important applications in various fields including Stackelberg games and moral hazard problems in economics ( [37,26]), hyperparameter selection and meta learning in machine learning ( [18-20, 14, 23, 24, 27, 28, 31]). More applications can be found in the monographs [3,10,13,36], the survey on bilevel optimization [9,12] and the references within. ...
Preprint
In this paper, we present difference of convex algorithms for solving bilevel programs in which the upper level objective functions are difference of convex functions, and the lower level programs are fully convex. This nontrivial class of bilevel programs provides a powerful modelling framework for dealing with applications arising from hyperparameter selection in machine learning. Thanks to the full convexity of the lower level program, the value function of the lower level program turns out to be convex and hence the bilevel program can be reformulated as a difference of convex bilevel program. We propose two algorithms for solving the reformulated difference of convex program and show their convergence under very mild assumptions. Finally we conduct numerical experiments to a bilevel model of support vector machine classification.
... As shown by [10], atx = 1, bothȳ 1 ...
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Article
A new numerical method is presented for bilevel programs with a nonconvex follower’s problem. The basic idea is to piecewise construct convex relaxations of the follower’s problems, replace the relaxed follower’s problems equivalently by their Karush–Kuhn–Tucker conditions and solve the resulting mathematical programs with equilibrium constraints. The convex relaxations and needed parameters are constructed with ideas of the piecewise convexity method of global optimization. Under mild conditions, we show that every accumulation point of the optimal solutions of the sequence approximate problems is an optimal solution of the original problem. The convergence theorems of this method are presented and proved. Numerical experiments show that this method is capable of solving this class of bilevel programs.
... However, compared with standard markets, the information shared among consumers and providers of medical care is asymmetric in the healthcare system, while consumers' autonomy in selecting medical service is relatively limited [10][11][12]. It is therefore noteworthy that when confronted with vastly intensified competition in the hospital market, hospitals might adopt the strategies for their own benefits at the sacrifice of compromising patients' interests, which is called the principal-agent problem according to the literature [13][14][15][16][17]. ...
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Article
With the implementation of a series of pro-competition policies in China, the hospital market competition has been intensified dramatically over the past decade. Based on previous literature, such competition is very much likely to bring about an upgoing trend in the promotion and expansion of medical facilities among hospitals as an essential strategy for attracting patients, which is known as Medical Arms Race (MAR). Comprehensive evaluations have been conducted by previous studies on the consequences of the MAR, which, however, merely provided inadequate empirical evidence on the relationship between hospital competition and MAR. Utilizing the variations in hospital competition across various regions and through different time periods in Sichuan Province as a prototype representative of the nationwide situation, a dynamic panel data model was established and adopted in this study for investigating whether intensified hospital competition had resulted in the expansion of medical facilities in China during the corresponding time period. The geopolitical boundaries and Herfindahl-Hirschman Index (HHI) were respectively employed to define the hospital market and measure the competition degree. We found that a 10% reduction in HHI is associated with an 8.79% increase in regional total costs of advanced medical equipment per capita, suggesting that hospital competition would lead to medical equipment expansion. Our results provide novel evidence on MAR which is particularly applicable for the healthcare system in China, providing suggestions for nationwide healthcare reform in order to mitigate potential negative outcomes induced by the implementation of pro-competition policies.
... It is shown in [967] that this approach is only possible if the lower-level problem is a convex one. Problem (20.4.6) is a so-called mathematical program with equilibrium (or complementarity) constraints (MPEC), see [897]. ...
Chapter
Bilevel optimization problems are hierarchical optimization problems where the feasible region of the so-called upper level problem is restricted by the graph of the solution set mapping of the lower level problem. Aim of this article is to collect a large number of references on this topic, to show the diversity of contributions and to support young colleagues who try to start research in this challenging and interesting field.
... Companies want to motivate purchasing agents to seek cost saving and better value for the organization (Nollett et al. 2008;Pohl and Foerstl 2011). These organizations also want to safeguard the legitimacy of real cost saving that contribute to the organization's success, while preventing the moral hazard of giving credit for savings, when credit isn't due (Mirrlees 1976(Mirrlees , 1999Nollett et al. 2008;Tchokogu e et al., 2017). In sum, cost saving are desirable; defining them can be murky. ...
Article
It is widely recognized that one of the purchasing function’s primary objectives is to generate cost saving through cost reduction and cost avoidance as it works with the supply base to provide high quality materials and services on a timely basis. This research develops mid‐range theory by incorporating empirical evidence and the tenets of agency theory to the specific domain of a purchasing agent working within an organization. This domain differs from other agency relationships because there are multiple principals with misaligned goals within the organization that influence how purchasing cost saving are counted and thus influence the impact of those savings on purchasing performance. Agency theory helps articulate propositions in this context by providing insight into how purchasing agents perform their organizational duties related to cost saving and avoiding cost increases. The focus is specifically on examining how the challenging area of cost avoidance savings are tracked, measured, and recognized. Case studies from eight organizations reveal that there is significant prospect for suboptimal performance due to the design of reward and measurement systems and the reluctance of purchasing to challenge these systems. However, this can be addressed through an investment in robust systems supported by top management and finance.
... ll affect on the behavior of one or more parties." The classic example is in the insurance industry, where coverage against a loss might increase the risk-taking behavior of the insured, See Investorwords website, at http://www.investorwords.com/3 l l 7 /moral~ hazard.html. For an interesting article relating to the issue of moral hazard, see J.A. Mirrlees. 1999 The main problem in this scenario is that such instant price deflation towards a certain designated level would be chosen not by the markets, as in most developed nations, but by government bureaucrats. 54 Latin meaning "let the buyer beware." 55 One of the well-known examples on incomplete information is "the parable of separate island ...
Article
Two years following the 1997-98 Korean financial crisis, the Korean government attempted to bolster consumer spending and re-invigorate the national economy by pursuing a series of policies that directly promoted the use of consumer credit cards. Subsequently, consumer credit card spiked upward, which led to a dramatic surge in individual debtor defaults. The government in response mode again thereafter initiated a three-pronged legislative effort to counter the post-1997 individual debtor polemic: (i) the Individual Debtor Rehabilitation Act (“IDRA” or the “Act”); (ii)) the Korea Asset Management Company’s Bad Bank (KAMCO or “Bad Bank”); and (iii) the Credit Counseling and Recovery Service (CCRS) (collectively, the “Legal Acts”). This paper surveys and analyzes the Legal Acts approach to resolving South Korea’s post-1997 consumer credit card spending polemic.
Article
Customary stochastic programming with recourse assumes that the probability distribution of random parameters is independent of decision variables. Recent studies demonstrated that stochastic programming models with endogenous uncertainty can better reflect many real-world activities and applications accompanying with decision-dependent uncertainty. In this paper, we concentrate on a class of decision-dependent two-stage stochastic programs (DTSPs) and investigate their discrete approximation. To develop the discrete approximation methods for DTSPs, we first derive the quantitative stability results for DTSPs. Based on the stability conclusion, we examine two discretization schemes when the support set of random variables is bounded, and give the rates of convergence for the optimal value and optimal solution set of the discrete approximation problem to those of the original problem. Then we extend the proposed approaches to the general situation with an unbounded support set by using the truncating technique. As an illustration of our discretization schemes, we reformulate the discretization problems under specific structures of the decision-dependent distribution. Finally, an application and numerical results are presented to demonstrate our theoretical results.
Book
There has been explosive progress in the economic theory of uncertainty and information in the past few decades. This subject is now taught not only in departments of economics but also in professional schools and programs oriented toward business, government and administration, and public policy. This book attempts to unify the subject matter in a simple, accessible manner. Part I of the book focuses on the economics of uncertainty; Part II examines the economics of information. This revised and updated second edition places a greater focus on game theory. New topics include posted-price markets, mechanism design, common-value auctions, and the one-shot deviation principle for repeated games.
Article
We study a class of models of moral hazard in which a principal contracts with a counterparty, which may have its own internal organizational structure. The principal has non‐Bayesian uncertainty as to what actions might be taken in response to the contract, and wishes to maximize her worst‐case payoff. We identify conditions on the counterparty's possible responses to any given contract that imply that a linear contract solves this maxmin problem. In conjunction with a Richness property motivated by much previous literature, we identify a Responsiveness property that is sufficient—and, in an appropriate sense, also necessary—to ensure that linear contracts are optimal. We illustrate by contrasting several possible models of contracting in hierarchies. The analysis demonstrates how one can distill key features of contracting models that allow their findings to be carried beyond the bilateral setting.
Article
This paper examined the effects of credit risk, intellectual capital as well as credit risk moderated by intellectual capital on financial performance of fifteen listed deposit money banks in Nigeria (DMBs) from 2007 to 2016. Data were sourced from annual reports of banks and Nigerian National Bureau of Statistics and analysed using Generalised Method of Moments (GMM). The study finds that credit risk index by loan loss ratio negatively affects financial performance of the sampled banks; while capital employed efficiency, loan loss provision moderated by intellectual capital, capital adequacy ratio, income and diversification have positive relationship with banks’ financial performance. Thus, the study recommends that banks should strengthen their credit risk management culture to ensure prompt repayment of loans. The banks should operate within the required capital adequacy ratio to serve as buffer against loan loss provisions provided by the Central Bank of Nigeria. A strong credit risk management culture should be embedded within intellectual capital structure of banks, where all persons at all levels appreciate and understand the banks’ risk management policies as well as strategies and incorporate same into decision-making and business processes.
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Article
Article
We study a compensation problem for salespeople with learning potential. In our model, both the firm and sales agent are risk neutral and forward-looking; the agent can privately observe his skill, exert effort, and learn from experience; the firm can learn from the agent’s choice and revise sales targets over time. The problem entails a dynamic tradeoff between exploiting learning, screening information, and maximizing efficiency. We find the optimal compensation plan differs substantially from the existing ones: it sets aggressive targets for expediting skill development, and pays the information rent for neutralizing the agent’s misbehaving temptation over the entire relationship. We find learning drives the long-run outcomes; ignoring it can mislead compensation design and inflict substantial losses. Our results shed light on when and why firms distort sales, favor incumbents, and prefer long-term plans. By highlighting the critical role of learning in long-run performance, this study advances our understanding of salesforce theory and practice. This paper was accepted by Juanjuan Zhang, marketing.
Article
Article
This paper investigates the presence of career and promotion-based incentives in the context of arm’s-length contracting between wineries and independent wine-grape farmers. We hypothesise that long-term contracts represent a stage in a farmer’s career after a series of short-term contracts. We develop a conceptual framework to frame the interaction between explicit performance incentives and implicit career incentives arising from the possibility of promotion to a long-term contract, conditional on wineries learning a farmer’s potential for superior-quality production. Based on data from Chilean wine-grape farmers, we find evidence suggesting that implicit market-based incentives, usually studied in the context of employment contracts, are also important in arm’s-length contracts used in procurement of farm output.
Article
This article proposes a methodology to calculate the effect of moral hazard on short term credit (working capital) to small and medium-sized enterprises (SMEs). The methodology incorporates four categories of moral hazard ratio defined in a previous study, which are employed to determine probability of default based on a logit model. To this end, a novel Colombian database is used to calculate a moral hazard index that considers the percentages of the odds ratios of the moral hazard variables for positive coefficients on the probabilities of default. The empirical analysis result in an index measuring the impact of moral hazard on odds ratio mainly based on underinvestment moral hazard category in the sample of analyzed companies for the period ranged from 2007 to 2014.
Thesis
This thesis is split into three parts. In the first part, we apply the Principal-Agent theory to some problems of market microstructure. First, we build an incentives mechanism to improve the market quality in the context of market-making activity in a lit and a dark pool managed by the same exchange. Then, we adapt the incentives design to the regulation of market-making activity when several market-makers compete in a liquidity platform. We also propose a form of incentives based on the choice of tick sizes on the bid and ask sides of a single asset. Next, we tackle the issue of designing a derivatives market, using a quantization method to select the options listed on the exchange and the Principal-Agent framework to create incentives for an option market-maker. Finally, we develop an incentives mechanism to increase the investment in green bonds, robust to model specification, and outperforming current tax-incentives policies of the governments.The second part of this thesis is dedicated to option market-making in high dimension. We first propose a framework a constant Greek assumption to deal with long-dated options. Then, we propose an approximation of the value function enabling to deal with time-varying Greeks and short-dated options. Finally, we develop a framework for the high-frequency dynamics of the implied volatility surface. Using multidimensional Hawkes processes, we show how this setting can reproduce easily well-known stylized facts such as the skew, smile and term structure of the surface.The last part of this thesis is devoted to optimal trading problems in high dimension. First, we develop a framework to tackle the smart order routing (SOR) problem taking into account non-stationarity of markets. For a large number of venues, we use a deep reinforcement learning approach to compute the optimal controls of the trader. Then, we present a methodology to solve approximately optimal trading problems without using stochastic control theory. We propose a framework in which a myopic agent exhibits approximately an optimal behavior if he uses the gradient of the high-level trajectory as short-term alpha. Finally, we present two new developments on the optimal execution literature. First, we show that we can obtain a closed-form solution for the Almgren-Chriss execution problem with geometric Brownian motion and quadratic penalty. Second, we propose an application of the latent order book model to the problem of optimal execution of a portfolio of assets, in the context of liquidity stress testing.
Full-text available
Thesis
Cette thèse de doctorat porte sur la modélisation de l’effort de prévention et de sa relation avec l’assurance de marché. Chacun des chapitres la composant, tente de capturer différents aspects de cette problématique, de l’étude d’un critère conforme aux pratiques actuarielles à celui du côté de l’offre en assurance, en passant par l’inclusion de biais de perception du risque et par une approche de la prévention en temps dynamique. Le chapitre 1 modélise la relation entre un assureur et un assuré sous la forme d’un jeu de Stackelberg. Dans ce jeu, l’assureur joue en premier en proposant un contrat d’assurance sous la forme d’un facteur de chargement. L’assuré joue ensuite en choisissant le taux de couverture et son effort de prévention optimaux. L’assuré comme l’assureur ont pour but de minimiser leurs mesures de risque respectives qui sont toutes deux cohérentes. Les effets respectifs de l’auto-assurance et l’auto-protection, sur la minimisation du risque seront étudiés. Dans chaque cas, il sera montré que les choix optimaux de l’assuré existent et le contrat optimal pour l’assureur sera caractérisé. De plus, il sera montré que si la mesure de risque de l’agent décroit plus rapidement que l’espérance de sa perte, alors l’effort optimal est croissant avec le facteur de chargement avec une discontinuité potentielle lorsque la couverture optimale passe de complète à nulle. Cependant, dans le cas contraire l’effort optimal peut être croissant ou décroissante en fonction du facteur de chargement. Le chapitre 2 étudie la relation entre auto-assurance et assurance de marché également sous la forme d’un problème d’optimisation pour un agent. De manière similaire au chapitre 1, cet agent doit déterminer le taux de couverture et l’effort de prévention qui réduiront de manière optimale sa mesure de risque. La mesure de risque considérée est dite de distorsion et est définie à partir d’une fonction de distorsion non concave. Ceci permet de tenir compte de biais cognitifs individuels potentiels dans la perception du risque. La caractérisation de la solution optimale pour l’agent permet d’apporter une nouvelle conclusion dans la relation entre auto-assurance et assurance de marché. L’auto-assurance n’est plus seulement substituable à l’assurance de marché, elle peut être également complémentaire à celle-ci, suivant la sensibilité de l’effort de prévention au prix de l’assurance. Le chapitre 3 se concentre sur l’auto-protection en proposant un problème de maximisation d’utilité espérée en version dynamique. Ceci se présente sous forme d’un problème de contrôle stochastique dans lequel l’agent choisit sa couverture assurantielle et son effort de prévention qui est dynamique. Le problème peut être séparé en deux sous-problèmes, le premier est une optimisation en l’effort et le second en la couverture assurantielle. Comme l’individu veut obtenir la richesse finale la plus importante possible, il cherche à maximiser l’espérance de l’utilité exponentielle de cette richesse. La richesse de l’agent peut être vue comme la solution d’une équation différentielle stochastique rétrograde à saut, cette équation admet une unique solution et qui est de plus explicite. En particulier, on obtient que l’effort optimal d’auto- protection est constant. La distribution initiale du processus de perte, quand il n’y a pas d’effort, est donnée par un processus de Poisson composé qui est notamment un processus de Lévy. Obtenir un effort optimal constant signifie donc que la propriété de Lévy des processus est préservée par la maximisation d’une espérance d’utilité exponentielle. L’analyse du problème en la couverture assurantielle donne une condition suffisante pour obtenir l’existence d’un niveau de couverture optimal. L’individu pourra alors souscrire à une assurance en fournissant un effort de prévention qui lui permettra de maximiser sa satisfaction ou bien choisir de ne pas souscrire au contrat mais en prenant toutefois part à des actions d’auto-protection
Chapter
This chapter deals with polylithic modeling and solution approaches. Such approaches allow to considerably extending the set of solvable practical problems both in their quality (structure) and in their size (the number of variables and constraints). These approaches are illustrated by problems from paper industry, which were solved with the help of polylithic modeling and solution approaches. In detail, roll minimization based on column generation, simultaneous minimization of waste, and the number of used patterns, as well as format production, are treated.
Article
In this paper, we propose an iterative algorithm to find the optimal incentive mechanism for the principal-agent problem under moral hazard where the number of agent action profiles is infinite, and where there are an infinite number of results that can be observed by the principal. This principal-agent problem has an infinite number of incentive-compatibility constraints, and we transform it into an optimization problem with an infinite number of constraints called a semi-infinite programming problem. We then propose an exterior penalty function method to find the optimal solution to this semi-infinite programming and illustrate the convergence of this algorithm. By analyzing the optimal solution obtained by the proposed penalty function method, we can obtain the optimal incentive mechanism for the principal-agent problem with an infinite number of incentive-compatibility constraints under moral hazard.
Article
Most information that public firms are required to disclose is relatively hard (e.g., historical information), whereas the disclosure of relevant information that is softer in nature (e.g., forward looking information) is typically left to firms’ discretion. The lack of a mandatory requirement to disclose soft information has been at the heart of a number of on-going accounting debates. This study shows that while mandating disclosure increases the frequency of disclosure, it results in a reduction in disclosure quality when information is soft. By exploring this tradeoff, the paper sheds light on the merits of restricting mandatory disclosure requirements to verifiable information and leaving disclosure of soft information unregulated. The value of leaving disclosure unregulated is shown to be maximized when managers are given bonus-based compensation, with minimum performance thresholds and maximum caps, similar to those documented in the literature.
Chapter
In this paper we study constraint qualifications and optimality conditions for bilevel programming problems. We strive to derive checkable constraint qualifications in terms of problem data and applicable optimality conditions. For the bilevel program with convex lower level program we discuss drawbacks of reformulating a bilevel programming problem by the mathematical program with complementarity constraints and present a new sharp necessary optimality condition for the reformulation by the mathematical program with a generalized equation constraint. For the bilevel program with a nonconvex lower level program we propose a relaxed constant positive linear dependence (RCPLD) condition for the combined program.
Chapter
We study optimistic bilevel optimization problems, where we assume the lower-level problem is convex with a nonempty, compact feasible region and satisfies a constraint qualification for all possible upper-level decisions. Replacing the lower-level optimization problem by its first-order conditions results in a mathematical program with equilibrium constraints (MPEC) that needs to be solved. We review the relationship between the MPEC and bilevel optimization problem and then survey the theory, algorithms, and software environments for solving the MPEC formulations.
Article
We consider discrete‐time dynamic principal–agent problems with continuous choice sets and potentially multiple agents. We prove the existence of a unique solution for the principal's value function only assuming continuity of the functions and compactness of the choice sets. We do this by a contraction mapping theorem and so also obtain a convergence result for the value function iteration. To numerically compute a solution for the problem, we have to solve a collection of static principal–agent problems at each iteration. As a result, in the discrete‐time setting solving the static problem is the difficult step. If the agent's expected utility is a rational function of his action, then we can transform the bi‐level optimization problem into a standard nonlinear program. The final results of our solution method are numerical approximations of the policy and value functions for the dynamic principal–agent model. We illustrate our solution method by solving variations of two prominent social planning models from the economics literature.
Chapter
In this chapter, simple and complex economic systems are compared. The concept of complexity in economic theory is presented along with the ways to measure complexity in an economy. Also, there is a description of the contribution of the concept of information to economic theory, to be found in the basic assumption of the prevalent economic thought about perfect information. The analysis continues describing how imperfect information and asymmetry create market failures. In conclusion, the analysis treats the various types of economic systems aiming at a better understanding of the distinction between complexity and diversity.
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Article
Two kinds of models for a productive organization are presented. In the first, both production and rewards are based on the performance of individuals, which is perfectly observed. Their abilities are not observable. Despite this, theorems are proved giving strong grounds for the equality of wages and marginal products unless there is monopsony in the labor market. This latter case is also discussed. The second model, which focuses on the imperfect observation of performance, allows interesting deductions about optimal payment schedules and organizational structure.
Article
This paper explores how far one can go in applying the modern theory of competitive equilibrium to the case of uncertainty. In the first part, the analyses of Arrow and Debreu are extended to the case in which different economic agents may have different information about the environment. The second part deals with the limitations of the Arrow-Debreu type of model, and discusses the difficulties associated with nonconvexities in the production of information, with information generated by spot markets, and with limitations on the computational capacities of economic agents. It is argued that the demand for liquidity arises from, among other things, the last two phenomena, and thus does not appear to be amenable to analysis by means of the "neoclassical" theory of competitive equilibrium.
Article
This paper seeks to survey the literature in economics, philosophy, mathematics, and statistics on the subject of choice among alternatives the consequences of which are not certain. Attention is centered on the suggested modes of describing uncertainty and on the theories of rational and actual behavior of in individuals making choices.
Article
This paper analyzes the role of incentives, risk, and information in determining the structure of employment contracts. In particular, we focus on the functions performed by piece rate versus time rate payment systems and by supervisors. The relative reliance on piece rates versus time rates is related to risk sharing, to the use of the payment system as a method of screening employees, and to differential information concerning the difficulties of the tasks being performed. The choice of payment system thus depends on the attitudes toward risk of workers and employers, effort supply elasticities, the sources and magnitude of the uncertainties, and the nature of the supervision used in the employment relation. The supervisor is viewed as monitoring inputs (enforcing contracts), screening individuals, obtaining information about the state of the world, etc. Their roles are related to the nonconvexities associated with information.
Article
This paper measures the relative importance of quality and quantity effects of corporate taxation on foreign direct investment. Quantity is affected if corporate taxes reduce the equilibrium stock of foreign capital in a given country. Quality effects arise if taxes decrease the extent to which investment contributes to the corporate tax base and the capital intensity of production. Depending on the sign of the quality effects, the detrimental welfare effects of corporate taxation are either mitigated or aggravated. We derive a number of hypotheses how corporate tax changes may affect the quality of investment. Our hypotheses are then tested using data from a large sample of European multinationals. With regard to corporate tax effects on the corporate tax base, we find that quality effects account for up to fourty per cent of the total effect. With regard to corporate tax effects on labour income, our results suggest that quality effects mitigate the negative quantity effect by nearly sixty percent (as corporate taxes strongly increase the labor intensity of production). An important implication is that governments should not exclusively care about the size of inbound FDI flows but also about their specific characteristics, i.e. their quality.
Article
At least from the time of Ricardo, economists have begun their investigations of how competitive markets work, how wages, rents and prices are determined, by a detailed examination of agriculture. Even today, agriculture is taken as the paradigm-and perhaps almost the only important example-of a truly competitive market (or at least this was the case until the widespread government intervention in this market). For a number of years I have been concerned with how competitive markets handle risk taking, and how risk affects real resource allocation. Risks in agriculture are clearly tremendously important, yet remarkably the traditional theoretical literature has avoided explicit treatment 3 of risk sharing in agricultural environments. The consequences of this are important. First, it makes suspect the traditional conclusions regarding sharecropping. Is it really true that sharecropping results in too low a supply of labour, because workers equate their share of output times the (value of the) marginal productivity of labour to the marginal disutility of work, whereas Pareto optimality requires the (value of the) marginal productivity of labour be equal to the marginal disutility of work? Or is it true, as Wicksell asserted, that there is no distincion between landlords hiring labour or labour renting land? Second, it leaves unanswered many of the important economic questions. How is the equilibrium share determined? Why have some economies (in the past or at present) used one distribution system, other economies used others? Our object is to formulate a simple general equilibrium model of a competitive agricultural economy. (Other general equilibrium models of competitive economies with uncertainty have been formulated by Arrow [2] and Debreu [9], Diamond [10], and Stiglitz [14]. Each of these has its serious limitations in describing the workings of the modern capitalist economy. (See Stiglitz [15]).) The model is of interest not only for extending our understanding of these simple economies but also in gaining some insight into the far more complex phenomena of shareholding in modern corporations. Our focus is on the risk sharing and incentive properties of alternative distribution systems. The analysis is divided into two parts. In the first, the amount of labour (effort) supplied by an individual is given, and the analysis focuses on the risk sharing aspects of
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This chapter discusses some intricacies and difficulties that arise in the real world operation of contingent claims markets. Insurance contracts are the most readily observable and perhaps the most important example of contingent claims markets in action. The purpose of insurance is to protect risk-averse individuals from suffering the full consequences of those actions on the part of nature that affect them unfavorably. Individuals have different incomes in different states of nature and may face different prices. Perfect insurance transfers income between states of nature, preserving marginal cost pricing when the income is spent. With an imperfect measurement of the states of nature, income transfers are conditional on what is observed rather than on the state of nature. Alternatively, one could alter prices to provide insurance.
The Optimal Structure of Incentives and Authority within an Organisation
• Ðð
ÐÐ (1976)The Optimal Structure of Incentives and Authority within an Organisation'. Bell Journal of Economics, 7, 105±31.
Incentives and Risk Sharing in Share Cropping'. Review of Economics Studies
• J E Stiglitz
Stiglitz, J. E. (1974)Incentives and Risk Sharing in Share Cropping'. Review of Economics Studies, 41, 219±56.