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Jan Dhaene

Jan Dhaene
KU Leuven | ku leuven · Department of Accountancy, Finance and Insurance (AFI)

full professor

About

301
Publications
68,563
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7,132
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Introduction
Welcome to my ResearchGate page. I am Jan Dhaene, professor of actuarial science at KU Leuven, Belgium. For more information about my cv, publications and teaching activities, please visit www.jandhaene.org
Additional affiliations
January 1986 - present
KU Leuven

Publications

Publications (301)
Article
Full-text available
In an insurance context, one is often interested in the distribution function of a sum of random variables. Such a sum appears when considering the aggregate claims of an insurance portfolio over a certain reference period. It also appears when considering discounted payments related to a single policy or a portfolio at different future points in t...
Article
Full-text available
This article develops a unifying framework for allocating the aggregate capital of a financial firm to its business units. The approach relies on an optimization argument, requiring that the weighted sum of measures for the deviations of the business unit's losses from their respective allocated capitals be minimized. The approach is fair insofar a...
Article
Full-text available
We introduce a new and easy-to-calculate measure for the expected degree of herd behavior or co-movement between stock prices. This forward looking measure is model-independent and based on observed option data. It is baptized the Herd Behavior Index (HIX).The degree of co-movement in a stock market can be determined by comparing the observed marke...
Article
Full-text available
Probability statements about future evolutions of financial and actuarial risks are expressed in terms of the 'real-world' probability measure P, whereas in an arbitrage-free environment, the prices of these traded risks can be expressed in terms of an equivalent martingale measure Q. The assumption of independence between financial and actuarial r...
Article
Full-text available
In arbitrage-free but incomplete markets, the equivalent martingale measure Q for pricing traded assets is not uniquely determined. A possible approach when it comes to choosing a particular pricing measure is to consider the one that is 'closest'to the physical probability measure P, where closeness is measured in terms of relative entropy. In thi...
Article
Full-text available
In this paper, we introduce the rich classes of conditional distortion (CoD) risk measures and distortion risk contribution (ΔCoD) measures as measures of systemic risk and analyze their properties and representations. The classes unify, and significantly extend, existing systemic risk measures such as the conditional Value-at-Risk, conditional Exp...
Article
Full-text available
A general class of fair dynamic valuations, which are model-consistent (mark-to-model), market-consistent (mark-to-market) and time-consistent, was introduced by Barigou et al. (2019) in a multi-period setting. In this paper, we generalize the convex hedging approach proposed in Dhaene et al. (2017) to a multi-period framework and investigate the r...
Presentation
Full-text available
In this presentation, we give an introduction to the fair valuations of insurance liabilities in a single period framework, combining market- consistency and model-consistency. An online course based on this presentation can be found at www.jandhaene.org (courses, valuation principles).
Presentation
Full-text available
Article
Full-text available
We consider n risks X 1 , X 2 , … , X n insured by a layer coverage with deductibles and limits given by ( d 1 , l 1 ) , … , ( d n , l n ) , respectively. We investigate the optimal allocation of insurance layers from the viewpoint of the insurer. We derive lower and upper bounds for the survival function of the smallest and largest claim amounts u...
Article
Hedging techniques have been widely adopted in market-consistent or fair valuation approach required by recent solvency regulations, to take into account the market prices of the hedgeable parts of insurance liabilities. In this study, we investigate the fair dynamic valuation of insurance liabilities, which are model-consistent (mark-to-model), ma...
Article
For an arbitrage-free market with a single underlying asset, we investigate conditions under which the consecutive price levels are comonotonic. Furthermore, for an arbitrage-free market with n assets we investigate the consequences of assuming comonotonicity of the vector containing the price levels of each asset at a single future date T. Althoug...
Article
Full-text available
The Belgian Law of 20 July 2007 has drastically changed the Belgian private health insurance sector by making individual contracts lifelong with the technical basis (i.e. actuarial assumptions) fixed at policy issue. The goal of the Law is to ensure the accessibility to supplementary health coverage in order to protect policyholders from discrimina...
Article
We investigate fair (market-consistent and actuarial) valuation of insurance liability cash-flow streams in continuous time. We first consider one-period hedge-based valuations, where in the first step, an optimal dynamic hedge for the liability is set up, based on the assets traded in the market and a quadratic hedging objective, while in the seco...
Article
In this paper, we investigate the fair valuation of insurance liabilities in a dynamic multi-period setting. We define a fair dynamic valuation as a valuation which is actuarial (mark-to-model for claims independent of financial market evolutions), market-consistent (mark-to-market for any hedgeable part of a claim) and time-consistent, extending t...
Article
Delong et al. (2018) presented a theory of fair (market-consistent and actuarial) valuation of insurance liability cash-flow streams in continuous time. In this paper, we investigate in detail two practical applications of our theory of fair valuation. In the first example, we consider the fair valuation of a terminal benefit which is contingent on...
Article
Full-text available
We investigate the construction of medical inflation indexes. Such indexes can be used to update premiums of lifelong health insurance contracts. We compare the accuracy of the medical indexes currently applied in Belgium for private health insurance contracts with product-specific experience-based indexes. The latter enable to better capture produ...
Article
Full-text available
This paper addresses systematic longevity risk in long-term insurance business. We analyze the consequences of working under unknown survival probabilities on the efficiency of the Law of Large Numbers and point out the need for appropriate and feasible risk management techniques. We propose a setting for risk sharing schemes between the insurer an...
Preprint
Conditional risk (co-risk) measures and risk contribution measures are increasingly used in quantitative risk analysis to evaluate the systemic risk that the failure (or loss) of a component spreads to other components or even to the entire system. Co-risk measures are conditional versions of measures usually employed to assess isolated risks, whil...
Preprint
Full-text available
Conditional risk (co-risk) measures and risk contribution measures are increasingly used in quantitative risk analysis to evaluate the systemic risk that the failure (or loss) of a component spreads to other components or even to the entire system. Co-risk measures are conditional versions of measures usually employed to assess isolated risks, whil...
Article
Full-text available
In this paper, we investigate the fair valuation of insurance liabilities in a dynamic multi-period setting. We define a fair dynamic valuation as a valuation which is actuarial (mark-to-model for claims independent of financial market evolutions), market-consistent (mark-to-market for any hedgeable part of a claim) and time-consistent, extending t...
Article
A general class of fair valuations which are both market-consistent (mark-to-market for any hedgeable part of a claim) and actuarial (mark-to-model for any claim that is independent of financial market evolutions) was introduced in Dhaene et al. [Insurance: Mathematics & Economics, 76, 14–27 (2017)] in a single period framework. In particular, the...
Preprint
Full-text available
A general class of fair valuations which are both market-consistent (mark-to-market for any hedgeable part of a claim) and actuarial (mark-to-model for any claim that is independent of financial market evolutions) was introduced in Dhaene et al. [Insurance: Mathematics & Economics, 76, 14-27 (2017)] in a single period framework. In particular, the...
Preprint
Full-text available
For an arbitrage-free market with a single underlying asset, we investigate conditions under which the consecutive price levels are comonotonic. Furthermore, for an arbitrage-free market with n assets we investigate the consequences of assuming comonotonicity of the vector containing the price levels of each asset at a single future date T. Althoug...
Article
Full-text available
We revisit the general problem of minimizing a separable convex function with both a budget constraint and a set of box constraints. This optimization problem arises naturally in many resource allocation problems in engineering, economics, finance and insurance. Existing literature tackles this problem by using the traditional Kuhn–Tucker theory, w...
Article
Full-text available
This paper proposes the use of convex lower bounds as approximation to evaluate the aggregation of risks, based on additive risk factor models in the multivariate generalized Gamma distribution context. We consider two types of additive risk factor model. In Model 1, the risk factors that contribute to the aggregation are deterministic. In Model 2,...
Article
In this paper, an efficient method is proposed which accelerates the computation of the optimal strikes in the comonotonic upper bound for the value of an arithmetic Asian option. Numerical applications are carried out in the setting of Heston’s model, in which the distribution function of the underlying asset price is not available in closed form....
Article
Full-text available
We investigate fair (market-consistent and actuarial) valuation of insurance liability cash-flow streams in continuous time. We first consider one-period hedge-based valuations, where in the first step, an optimal dynamic hedge for the liability is set up, based on the assets traded in the market and a quadratic hedging objective, while in the seco...
Article
Full-text available
Delong et al. (2018) presented a theory of fair (market-consistent and actuarial) valuation of insurance liability cash-flow streams in continuous time. In this paper, we investigate in detail two practical applications of our theory of fair valuation. In the first example, we consider the fair valuation of a terminal benefit which is contingent on...
Article
Full-text available
In this paper, we investigate the fair valuation of liabilities related to an insurance policy or portfolio in a single period framework. We define a fair valuation as a valuation which is both market-consistent (mark-to-market for any hedgeable part of a claim) and actuarial (mark-to-model for any claim that is independent of financial market evol...
Article
Full-text available
This paper considers the problem of a lifelong health insurance cover where medical inflation is not sufficiently incorporated in the level premium determined at policy issue. We focus on the setting where changes in health benefits, driven by medical inflation, are accounted for by an appropriate update or indexation of the level premium, the poli...
Article
Full-text available
This paper proposes a practical way for indexing level premiums in lifelong medical insurance contracts, in order to take into account observed medical inflation. The indexing can be achieved by considering only premiums, without explicit reference to reserves. This appears to be relevant in practice as reserving mechanisms may not be transparent t...
Article
Full-text available
Les raisons de l'élaboration de la loi du 25 juin 1992 sur le contrat d'assurance terrestre (LCAT, qui a aujourd'hui fait place à la loi relative aux assurances du 4 avril 2014) s'ex-pliquent par la volonté du législateur de rétablir un équilibre entre assureur et consommateur. Elle remplaçait une loi antérieure datant du 11 juin 1874 qui ne compor...
Article
Abstract Let X 1,…, X n be a set of n continuous and non-negative random variables, with log-concave joint density function f, faced by a person who seeks for an optimal deductible coverage for these n risks. Let d=(d 1,… d n) and d∗=(d 1∗,… d n∗) be two vectors of deductibles such that d∗ is majorized by d. It is shown that∑ i= 1 n (X i∧ d i∗) is...
Article
Full-text available
In this paper, we extend the concept of mutual exclusivity proposed by [Dhaene, J. & Denuit, M. (1999). The safest dependence structure among risks. Insurance: Mathematics and Economics 25, 11–21] to its tail counterpart and baptize this new dependency structure as tail mutual exclusivity. Probability levels are first specified for each component o...
Article
Full-text available
Since the financial crisis of 2008, next to banks, insurers have received increasing attention from researchers and regulators because of their crucial role in the financial system. A key point for a stable insurer is its capital structure, i.e. the choice between equity, debt and provisions in financing its operations. Based on earlier work a quic...
Article
Full-text available
In this paper, we introduce two classes of indices which can be used to measure the market perception concerning the degree of dependency that exists between a set of random variables, representing different stock prices at a fixed future date. The construction of these measures is based on the theory of comonotonicity. Both types of herd behavior...
Article
Full-text available
Although VaR is important due to its widespread usage to obtain overall Solvency Capital Requirement (SCR) in the standard model of Solvency II directives, it is not subadditive. Without subadditivity, the summation of SCRs of different lines of business, which is used usually by risk managers, may underestimate overall SCR for an insurance company...
Article
In this paper, we investigate an optimization problem related to super-replicating strategies for European-type call options written on a weighted sum of asset prices, following the initial approach in Chen et al. (2008). Three issues are investigated. The first issue is the (non-)uniqueness of the optimal solution. The second issue is the generali...
Technical Report
Full-text available
The computation of various risk metrics is essential to the quantitative risk management of variable annuity guaranteed benefits. The current market practice of Monte Carlo simulation often requires intensive computations, which can be very costly for insurance companies to implement and take so much time that they cannot obtain information and tak...
Article
Full-text available
The computation of various risk metrics is essential to the quantitative risk management of variable annuity guaranteed benefits. The current market practice of Monte Carlo simulation often requires intensive computations, which can be very costly for insurance companies to implement and take so much time that they cannot obtain information and tak...
Article
Full-text available
In this paper, we extend the concept of mutual exclusivity proposed by Dhaene and Denuit (1999) to its tail counterpart and baptise this new dependency structure as tail mutual exclusivity. Probability levels are first specified for each component of the random vector. Under this dependency structure, at most one exceedance over the corresponding V...
Chapter
In the individual risk model, the total claims amount on a portfolio of insurance contracts is the random variable of interest. The total claims is modeled as the sum of all claims on the individual policies, which are assumed independent. We present several techniques, such as convolution and recursions, to obtain results in this model. Keywords:...
Article
Premiums and benefits associated with traditional life insurance contracts are usually specified as fixed amounts in policy conditions. However, reserve-dependent surrender values and reserve-dependent expenses are common in insurance practice. The famous Cantelli theorem in life insurance ensures that under appropriate assumptions surrendering can...
Article
To evaluate the aggregate risk in a financial or insurance portfolio, a risk analyst has to calculate the distribution function of a sum of random variables. As the individual risk factors are often positively dependent, the classical convolution technique will not be sufficient. On the other hand, assuming a comonotonic dependence structure will l...
Article
In this article, we show that some important implications concerning comonotonic couples and corresponding convex order relations for their sums cannot be translated to counter-monotonicity in general. In a financial context, it amounts to saying that merging counter-monotonic positions does not necessarily reduce the overall level of risk. We prop...
Article
Full-text available
We revisit the problem of minimizing a separable convex function with a linear constraint and box constraints. This optimization problem arises naturally in many optimal allocation problems in economics, finance and insurance. Existing literature exclusively tackles this problem by using the traditional Kuhn-Tucker theory, which leads to either ite...
Article
The regulator that is required to approve the statistical model and its parameters relies on the data that the insurance company provides. In case the regulator approves the model, he has some responsibility for it. The inability to validate the model, due to lack of resources or lack of understanding, causes the regulator to reject the proposed in...
Article
Full-text available
For lifelong health insurance covers, medical inflation not incorporated in the level premiums determined at policy issue requires an appropriate increase of these premiums and/or the corresponding reserves during the term of the contract. In this paper, we investigate
Article
Full-text available
In this paper we derive expressions for the Tail Variance and the Tail Variance Premium of risks in a multivariate log-elliptical setting. The theoretical results are illustrated by considering lognormal and log-Laplace distributions. We also derive approximate expressions for a Tail Variance -based allocation rule in a multivariate lognormal set-t...
Article
In this paper we show that under appropriate moment conditions, the supermodular ordered random vectors and with equal expected utilities (or distorted expectations) of the sums and for an appropriate utility (or distortion) function, must necessarily be equal in distribution, that is . The results in this paper can be considered as generalizations...
Article
Full-text available
In order to price multivariate derivatives, there is need for a multivariate stock price model. To keep the simplicity and attractiveness of the one-dimensional Black & Scholes model, one often considers a multivariate model where each individual stock follows a Black & Scholes model, but the underlying Brownian motions might be correlated. Althoug...
Article
We revisit the problem of minimizing a separable convex function with a linear constraint and box constraints. This optimization problem arises naturally in many applications in economics, insurance, and finance. Existing literature exclusively tackles this problem by using the traditional Kuhn-Tucker theory, which leads to either iterative schemes...
Article
We revisit the problem of minimizing a separable convex function with a linear constraint and box constraints. This optimization problem arises naturally in many applications in economics, insurance, and finance. Existing literature exclusively tackles this problem by using the traditional Kuhn-Tucker theory, which leads to either iterative schemes...
Article
Full-text available
Distorted expectations can be expressed as weighted averages of quantiles. In this note, we show that this statement is true, but that one has to be careful with the correct formulation of it. Furthermore, the proofs of the additivity property for distorted expectations of a comonotonic sum that appear in the literature often do not cover the case...