Beatriz Balbás

University of Castilla-La Mancha · Department of Economic Analysis and Finances

The combination of stochastic derivative pricing models and downside risk measures often leads to the paradox (risk, return) = (−infinity, +infinity) in a portfolio choice problem. The construction of a portfolio of derivatives with high expected returns and very negative downside risk (henceforth “golden strategy”) has only been studied if all the...

The combination of stochastic derivative pricing models and downside risk measures often leads to the paradox (risk,return)=(-infinity,+infinity) in a portfolio choice problem. The construction of a portfolio of derivatives with high expected return and very negative downside risk (henceforth "golden strategy") has been only studied if all the invo...

Downside risk measures play a very interesting role in risk management problems. In particular, the value at risk (VaR) and the conditional value at risk (CVaR) have become very important instruments to address problems such as risk optimization, capital requirements, portfolio selection, pricing and hedging issues, risk transference, risk sharing,...

The objective of this paper is twofold. On the one hand, the optimal combination of reinsurance and financial investment will be studied under a general framework. Indeed, there is no specific type of reinsurance contract, there is no specific dynamics of the involved financial instruments and the financial market does not have to be free of fricti...

This paper deals with a multiobjective portfolio selection problem involving expected wealth (or return), coherent risk measures, deviation measures, and “level II order book data”, i.e., natural restrictions provoked by the existence of several levels of both bid and ask quotes with the corresponding depth. Obviously, the incorporation of the orde...

This paper will deal with the optimal reinsurance problem and will involve the goals of both insurer and reinsurer. In particular, the study will incorporate the initial (before reinsurance) risk that the reinsurer uses in order to diversify (or hedge) the risk ceded by the insurer, general methods to prevent the reinsurer moral hazard will be exte...

The omega ratio is an interesting performance measure because it focuses on both downside losses and upside gains, and actuarial/financial instruments are reflecting more and more asymmetry and heavy tails. This paper focuses on the omega ratio optimization in general Banach spaces, which applies for both infinite-dimensional approaches and more cl...

This paper deals with the construction of “smooth good deals” (SGD), i.e., sequences of self-financing strategies whose global risk diverges to minus infinity and such that every security in every strategy of the sequence is a “smooth” derivative with a bounded delta. Since delta is bounded, digital options are excluded. In fact, the pay-off of eve...

The Value at Risk (VaR) is a very important risk measure for practitioners, supervisors and researchers. Many practitioners draw on VaR as a critical instrument in Risk Management and other Actuarial/Financial problems, while supervisors and regulators must deal with VaR due to the Basel Accords and Solvency II, among other reasons. From a theoreti...

VaR minimization is a complex problem playing a critical role in many actuarial and financial applications of mathematical programming. The usual methods of convex programming do not apply due to the lack of sub-additivity. The usual methods of differentiable programming do not apply either, due to the lack of continuity. Taking into account that t...

Recent literature has demonstrated the existence of an unbounded risk premium if one combines the most important models for pricing and hedging derivatives with coherent risk measures. There may exist combinations of derivatives (good deals) whose pair (return; risk) converges to the pair(+∞, −∞). This paper goes beyond existence properties and loo...

This paper deals with portfolio selection problems under risk and ambiguity. The investor may be ambiguous with respect to the set of states of nature and their probabilities. Both static and discrete or continuous time dynamic pricing models are included in the analysis. Risk and ambiguity are measured in general settings. The considered risk meas...

The so-called Problem of Optimal Premium Calculation deals with the selection of the appropriate premiums to be paid by the insurance policies. At first sight, this seems to be a statistical estimation problem: we should estimate the mean claim amount, which in actuarial terms is known as the net premium. Nevertheless, several extensions of this pr...

This paper deals with the optimal reinsurance problem if both insurer and reinsurer are facing risk and uncertainty, though the classical uncertainty free case is also included. The insurer and reinsurer degrees of uncertainty do not have to be identical. The decision variable is not the retained (or ceded) risk, but its sensitivity with respect to...

This paper proposes risk sharing strategies, which allow insurers to cooperate and diversify non-systemic risk. We deal with both deviation measures and coherent risk measures and provide general mathematical methods applying to optimize them all. Numerical examples are given in order to illustrate how efficiently the non-systemic risk can be diver...

This paper studies an optimization problem involving pay-offs of (perhaps dynamic) investment strategies. The pay-off is the decision variable, the expected pay-off is maximized and its risk is minimized. The pricing rule may incorporate transaction costs and the risk measure is continuous, coherent and expectation bounded. We will prove the necess...

Recent literature has proved that many classical very important pricing models of Financial Economics (Black and Scholes, Heston, etc.) and risk measures (VaR, CVaR, etc.) may lead to “pathological meaningless situations”, since there exist sequences of portfolios whose negative risk and positive expected return are unbounded. Such a sequence of st...

In this paper we calculate premiums which are based on the minimization of the Expected Tail Loss or Conditional Tail Expectation (CTE) of absolute loss functions. The methodology generalizes well known premium calculation procedures and gives sensible results in practical applications. The choice of the absolute loss becomes advisable in this cont...

The optimal reinsurance problem is a classic topic in actuarial mathematics. Recent approaches consider a coherent or expectation bounded risk measure and minimize the global risk of the ceding company under adequate constraints. However, there is no consensus about the risk measure that the insurer must use, since every risk measure presents advan...

The minimization of risk functions is becoming a very important topic due to its interesting applications in Mathematical Finance and Actuarial Mathematics. This paper addresses this issue in a general framework. Many types of risk function may be involved. A general representation theorem of risk functions is used in order to transform the initial...

The paper deals with optimal portfolio choice problems when risk levels are given by coherent risk measures, expectation bounded risk measures or general deviations. Both static and dynamic pricing models may be involved. Unbounded problems are characterized by new notions such as (strong) compatibility between prices and risks. Surprisingly, the l...

The minimization of risk functions is becoming very important due to its interesting applications in Mathematical Finance and Actuarial Mathematics. This paper addresses this issue in a general framework. Vector optimization problems involving many types of risk functions are studied. The “balance space approach” of multiobjective optimization and...

Estudiaremos el problema de la valoración de contratos de seguro ligados al mercado financiero, tales como las anualidades o rentas ligadas a índices bursátiles. Introduciremos un principio de prima basado en la optimización de medidas de riesgo coherentes y acotadas por la media. Este principio parece presentar una serie de propiedades de interés....

This paper studies the optimal reinsurance problem when risk is measured by a general risk measure. Necessary and sufficient optimality conditions are given for a wide family of risk measures, including deviation measures, expectation bounded risk measures and coherent measures of risk. The optimality conditions are used to verify whether the class...

A new, non-statistical method is presented for analysis of the past history and current evolution of economic and financial processes. The method is based on the sliding model approach using linear differential or difference equations applied to discrete information in the form of known chronological data (time series) about the process. An algorit...

Risk measures beyond the variance have shown theoretical advantages when addressing some classical problems of Financial Economics, at least if asymmetries and/or heavy tails are involved. Nevertheless, in portfolio selection they have provoked several caveats such as the existence of good deals in most of the arbitrage free pricing models. In othe...

The optimal reinsurance problem is a classic topic in Actuarial Mathematics. Recent approaches consider a coherent or expectation bounded risk measure and minimize the global risk of the ceding company under adequate constraints. However, there is no consensus about the risk measure that the insurer must use, since every risk measure presents advan...

The paper studies the optimal reinsurance problem if the risk level is measured by a general risk function. Necessary and sufficient optimality conditions are given for a wide family of risk functions, including Deviation Measures, Expectation Bounded Risk Measures and Coherent Measures of Risk. Then the optimality conditions are used to verify whe...