%0 Journal Article %J Statistics & Risk Modeling %D Accepted %T Bounds on Choquet Risk Measures in Finite Product Spaces with Ambiguous Marginals %A Ghossoub, M. %A Saunders, D. %A Zhang, K.S. %B Statistics & Risk Modeling %G eng %0 Journal Article %J Mathematics of Operations Research %D Accepted %T (No-)Betting Pareto Optima under Rank-Dependent Utility %A Beissner, P. %A Boonen, T. %A Ghossoub, M. %B Mathematics of Operations Research %G eng %0 Journal Article %J Journal of Risk and Insurance %D Accepted %T Pareto-Efficient Risk Sharing in Centralized Insurance Markets with Application to Flood Risk %A T.J. Boonen %A A. Chong %B Journal of Risk and Insurance %G eng %0 Journal Article %J Scandinavian Actuarial Journal %D 2024 %T Pareto-Optimal Insurance with an Upper Limit on the Insurer's Exposure %A Coke, O %A Ghossoub, M %A Zhu, M %B Scandinavian Actuarial Journal %V 2024 %P 227-251 %G eng %N 3 %0 Journal Article %J Insurance: Mathematics and Economics %D 2024 %T Stackelberg Equilibria with Multiple Policyholders %A Ghossoub, M. %A Zhu, M.B. %B Insurance: Mathematics and Economics %V 116 %P 189-201 %G eng %N 1 %0 Journal Article %J European Journal of Operational Research %D 2023 %T Bowley vs. Pareto Optima in Reinsurance Contracting %A Boonen, T.J. %A Ghossoub, M. %B European Journal of Operational Research %V 307 %P 382-391 %G eng %U https://www.sciencedirect.com/science/article/abs/pii/S0377221722006476?via%3Dihub %N 1 %0 Journal Article %J Insurance: Mathematics and Economics %D 2023 %T Equilibria and Efficiency in a Reinsurance Market %A Zhu, M.B. %A Ghossoub, M. %A Boonen, T.J. %B Insurance: Mathematics and Economics %V 113 %P 24-49 %G eng %N 1 %0 Journal Article %J Mathematics of Operations Research %D 2023 %T Maximum Spectral Measures of Risk with given Risk Factor Marginal Distributions %A Mario Ghossoub %A Jesse Hall %A David Saunders %B Mathematics of Operations Research %V 48 %P 1158-1182 %G eng %N 2 %0 Journal Article %J European Actuarial Journal %D 2023 %T Optimal Insurance for a Prudent Decision-Maker under Heterogeneous Beliefs %A Ghossoub, M. %A Jiang, W. %A Ren, J. %B European Actuarial Journal %V 13 %P 703-730 %G eng %N 2 %0 Journal Article %J Finance and Stochastics %D 2023 %T Optimal Insurance under Maxmin-Expected-Utility %A Birghila, C. %A Boonen, T.J. %A Ghossoub, M. %B Finance and Stochastics %V 27 %P 467-501 %G eng %U https://link.springer.com/article/10.1007/s00780-023-00497-y %N 2 %0 Journal Article %J Insurance: Mathematics and Economics %D 2022 %T Pareto-Optimal Reinsurance under Individual Risk Constraints %A Ghossoub, M. %A Jiang, W. %A Ren, J. %B Insurance: Mathematics and Economics %V 107 %P 307-325 %G eng %0 Journal Article %J Journal of Economic Theory %D 2021 %T Aggregation of Opinions and Risk Measures %A Massimiliano Amarante %A Mario Ghossoub %B Journal of Economic Theory %V 196 %G eng %U https://www.sciencedirect.com/science/article/abs/pii/S0022053121001277 %0 Journal Article %J Insurance: Mathematics and Economics %D 2021 %T Comparative Risk Aversion in RDEU with Applications to Optimal Underwriting of Securities Issuance %A Mario Ghossoub %A Xuedong He %B Insurance: Mathematics and Economics %V 101 %P 6-22 %G eng %U https://www.sciencedirect.com/science/article/abs/pii/S0167668720300871 %N 1 %0 Journal Article %J Economic Theory Bulletin %D 2021 %T On the Continuity of the Feasible Set Mapping in Optimal Transport %A M. Ghossoub %A D. Saunders %B Economic Theory Bulletin %G eng %U https://link.springer.com/article/10.1007/s40505-021-00199-8 %0 Journal Article %J Insurance: Mathematics and Economics %D 2021 %T Optimal Reinsurance with Multiple Reinsurers: Distortion Risk Measures, Distortion Premium Principles, and Heterogeneous Beliefs %A Tim Boonen %A Mario Ghossoub %B Insurance: Mathematics and Economics %V 101 %P 23-37 %G eng %U https://www.sciencedirect.com/science/article/abs/pii/S0167668720300883 %N 1 %0 Journal Article %J ASTIN Bulletin %D 2020 %T Bilateral Risk Sharing with Heterogeneous Beliefs and Exposure Constraints %A Tim Boonen %A Mario Ghossoub %B ASTIN Bulletin %V 50 %P 293-323 %G eng %U https://www.cambridge.org/core/journals/astin-bulletin-journal-of-the-iaa/article/bilateral-risk-sharing-with-heterogeneous-beliefs-and-exposure-constraints/96919FC90D5D9091B1592464720A1E16 %N 1 %0 Journal Article %J Scandinavian Actuarial Journal %D 2020 %T Budget-Constrained Optimal Retention With an Upper Limit on the Retained Loss %A Mario Ghossoub %B Scandinavian Actuarial Journal %V 2020 %P 245-271 %G eng %U https://www.tandfonline.com/doi/full/10.1080/03461238.2019.1659177 %N 3 %0 Journal Article %J Insurance: Mathematics and Economics %D 2019 %T Budget-Constrained Optimal Insurance with Belief Heterogeneity %B Insurance: Mathematics and Economics %V 89 %P 79-91 %G eng %U https://www.sciencedirect.com/science/article/pii/S0167668719303907 %N 1 %0 Journal Article %J Insurance: Mathematics and Economics %D 2019 %T Budget-Constrained Optimal Insurance Without the Nonnegativity Constraint on Indemnities %A Mario Ghossoub %B Insurance: Mathematics and Economics %V 84 %P 22-39 %8 Jan 2019 %G eng %U https://www.sciencedirect.com/science/article/pii/S016766871730389X?via%3Dihub %N 1 %0 Journal Article %J Insurance: Mathematics and Economics %D 2019 %T On the Existence of a Representative Reinsurer under Heterogeneous Beliefs %A Tim Boonen %A Mario Ghossoub %B Insurance: Mathematics and Economics %V 88 %P 209-225 %G eng %U https://www.sciencedirect.com/science/article/pii/S0167668718305365 %0 Journal Article %J Insurance: Mathematics and Economics %D 2019 %T Optimal Insurance under Rank-Dependent Expected Utility %A Mario Ghossoub %B Insurance: Mathematics and Economics %V 87 %P 51-66 %G eng %U https://www.sciencedirect.com/science/article/pii/S0167668718302531?via%3Dihub %N 1 %0 Journal Article %J Mathematics and Financial Economics %D 2018 %T A Neyman-Pearson Problem with Ambiguity and Nonlinear Pricing %A Ghossoub, M. %X

We consider a problem of the Neyman-Pearson type arising in the theory of portfolio choice in the presence of probability weighting, such as in markets with Choquet pricing (as in Araujo et al (2011), Cerreia-Vioglio et al (2015), Chateauneuf and Cornet (2015), or Chateauneuf et al (1996)) and ambiguous beliefs about the payoffs of contingent claims. Specifically, we consider a problem of optimal choice of a contingent claim so as to minimize a non-linear pricing functional (or a distortion risk measure), subject to a minimum expected performance measure (or a minimum expected return or utility), where expectations with respect to distorted probabilities are taken in the sense of Choquet. Such contingent claims are called cost-efficient. We give an analytical characterization of cost-efficient contingent claims under very mild assumptions on the probability weighting functions, thereby extending some of the results of Ghossoub (2016), and we provide examples of some special cases of interest. In particular, we show how a cost-efficient contingent claim exhibits a desirable monotonicity property: It is anti-comonotonic with the random mark-to-market value (or return, etc.) of the underlying financial position, and it is hence a hedge against such variability.

%B Mathematics and Financial Economics %V 12 %P 365-385 %G eng %U https://link.springer.com/article/10.1007%2Fs11579-017-0207-y %N 3 %0 Journal Article %J North American Actuarial Journal %D 2017 %T Arrow's Theorem of the Deducible with Heterogeneous Beliefs %A M Ghossoub %X

In Arrow's classical problem of demand for insurance indemnity schedules, it is well-known that the optimal insurance indemnification for an insurance buyer—or decision maker (DM)—is a deductible contract when the insurer is a risk-neutral Expected-Utility (EU) maximizer and when the DM is a risk-averse EU maximizer. In Arrow's framework, however, both parties share the same probabilistic beliefs about the realizations of the underlying insurable loss. This article reexamines Arrow's problem in a setting where the DM and the insurer have different subjective beliefs. Under a requirement of compatibility between the insurer's and the DM's subjective beliefs, we show the existence and monotonicity of optimal indemnity schedules for the DM. The belief compatibility condition is shown to be a weakening of the assumption of a monotone likelihood ratio. In the latter case, we show that the optimal indemnity schedule is a variable deductible schedule, with a state-contingent deductible that depends on the state of the world only through the likelihood ratio. Arrow's classical result is then obtained as a special case.

%B North American Actuarial Journal %V 21 %P 15-35 %G eng %U http://www.tandfonline.com/doi/full/10.1080/10920277.2016.1192477 %N 1 %0 Journal Article %J Economic Journal %D 2017 %T Contracting on Ambiguous Prospects %A M. Amarante %A M. Ghossoub %A E.S Phelps %X

We study contracting problems where one party perceives ambiguity about the relevant contingencies. We show that the party who perceives ambiguity has to observe only the revenue/loss generated by the prospect object of negotiation, but not the underlying state. We, then, introduce a novel condition (vigilance), which extends the popular monotone likelihood ratio property to settings featuring ambiguity. Under vigilance, optimal contracts are monotonic and, thus, produce the right incentives in the presence of both concealed information and hidden actions. Our result holds irrespectively of the party's attitude towards ambiguity. Sharper results obtain in the case of global ambiguity-loving behaviour.

%B Economic Journal %V 127 %P 2241-2262 %G eng %U http://onlinelibrary.wiley.com/doi/10.1111/ecoj.12381/abstract %N 606 %0 Journal Article %J Mathematics and Financial Economics %D 2016 %T Cost-Efficient Contingent Claims with Market Frictions %A M Ghossoub %X

In complete frictionless securities markets under uncertainty, it is well-known that in the absence of arbitrage opportunities, there exists a unique linear positive pricing rule, which induces a state-price density (e.g., Harrison and Kreps (1979)). Dybvig (1988) showed that the cheapest way to acquire a certain distribution of a consumption bundle (or security) is when this bundle is anti-comonotonic with the state-price density, i.e., arranged in reverse order of the state-price density. In this paper, we look at extending Dybvig’s ideas to complete markets with imperfections represented by a nonlinear pricing rule (e.g., due to bid-ask spreads). We consider an investor in a securities market where the pricing rule is “law-invariant” with respect to a capacity (e.g., Choquet pricing as in Araujo et al. (2011), Chateauneuf et al. (1996), Chateauneuf and Cornet (2015), Cerreia-Vioglio et al. (2015). The investor holds a security with a random payoff X and his problem is that of buying the cheapest contingent claim Y on X, subject to some constraints on the performance of the contingent claim and on its level of risk exposure. The cheapest such claim is called cost-efficient. If the capacity satisfies standard continuity and a property called strong diffuseness introduced in Ghossoub (2015), we show the existence and monotonicity of cost-efficient claims, in the sense that a cost-efficient claim is anti-comonotonic with the underlying security’s payoff X. Strong diffuseness is satisfied by a large collection of capacities, including all distortions of diffuse probability measures. As an illustration, we consider the case of a Choquet pricing functional with respect to a capacity and the case of a Choquet pricing functional with respect to a distorted probability measure. Finally, we consider a simple example in which we derive an explicit analytical form for a cost-efficient claim.

%B Mathematics and Financial Economics %V 10 %P 87-111 %G eng %U https://link.springer.com/article/10.1007/s11579-015-0151-7 %N 1 %0 Journal Article %J Risks %D 2016 %T Optimal Insurance for a Minimal Expected Retention: The Case of an Ambiguity-Seeking Insurer %A M. Amarante %A M Ghossoub %X

In the classical expected utility framework, a problem of optimal insurance design with a premium constraint is equivalent to a problem of optimal insurance design with a minimum expected retention constraint. When the insurer has ambiguous beliefs represented by a non-additive probability measure, as in Schmeidler, this equivalence no longer holds. Recently, Amarante, Ghossoub and Phelps examined the problem of optimal insurance design with a premium constraint when the insurer has ambiguous beliefs. In particular, they showed that when the insurer is ambiguity-seeking, with a concave distortion of the insured’s probability measure, then the optimal indemnity schedule is a state-contingent deductible schedule, in which the deductible depends on the state of the world only through the insurer’s distortion function. In this paper, we examine the problem of optimal insurance design with a minimum expected retention constraint, in the case where the insurer is ambiguity-seeking. We obtain the aforementioned result of Amarante, Ghossoub and Phelps and the classical result of Arrow as special cases.

%B Risks %V 4 %P 8 %G eng %U http://www.mdpi.com/2227-9091/4/1/8 %0 Journal Article %J Risks %D 2016 %T Optimal Insurance with Heterogeneous Beliefs and Disagreement about Zero-Probability Events %A M Ghossoub %X

In problems of optimal insurance design, Arrow’s classical result on the optimality of the deductible indemnity schedule holds in a situation where the insurer is a risk-neutral Expected-Utility (EU) maximizer, the insured is a risk-averse EU-maximizer, and the two parties share the same probabilistic beliefs about the realizations of the underlying insurable loss. Recently, Ghossoub re-examined Arrow’s problem in a setting where the two parties have different subjective beliefs about the realizations of the insurable random loss, and he showed that if these beliefs satisfy a certain compatibility condition that is weaker than the Monotone Likelihood Ratio (MLR) condition, then optimal indemnity schedules exist and are nondecreasing in the loss. However, Ghossoub only gave a characterization of these optimal indemnity schedules in the special case of an MLR. In this paper, we consider the general case, allowing for disagreement about zero-probability events. We fully characterize the class of all optimal indemnity schedules that are nondecreasing in the loss, in terms of their distribution under the insured’s probability measure, and we obtain Arrow’s classical result, as well as one of the results of Ghossoub as corollaries. Finally, we formalize Marshall’s argument that, in a setting of belief heterogeneity, an optimal indemnity schedule may take “any”shape.

%B Risks %V 4 %P 29 %G eng %U http://www.mdpi.com/2227-9091/4/3/29 %0 Journal Article %J Journal of Mathematical Economics %D 2015 %T Ambiguity on the Insurer's Side: The Demand for Insurance %A M. Amarante %A M. Ghossoub %A E.S Phelps %X

Empirical evidence suggests that ambiguity is prevalent in insurance pricing and underwriting, and that often insurers tend to exhibit more ambiguity than the insured individuals (e.g., Hogarth and Kunreuther, 1989). Motivated by these findings, we consider a problem of demand for insurance indemnity schedules, where the insurer has ambiguous beliefs about the realizations of the insurable loss, whereas the insured is an expected-utility maximizer. We show that if the ambiguous beliefs of the insurer satisfy a property of compatibility with the non-ambiguous beliefs of the insured, then optimal indemnity schedules exist and are monotonic. By virtue of monotonicity, no ex-post moral hazard issues arise at our solutions (e.g., Huberman et al., 1983). In addition, in the case where the insurer is either ambiguity-seeking or ambiguity-averse, we show that the problem of determining the optimal indemnity schedule reduces to that of solving an auxiliary problem that is simpler than the original one in that it does not involve ambiguity. Finally, under additional assumptions, we give an explicit characterization of the optimal indemnity schedule for the insured, and we show how our results naturally extend the classical result of Arrow (1971) on the optimality of the deductible indemnity schedule.

%B Journal of Mathematical Economics %V 58 %P 61-78 %G eng %U http://www.sciencedirect.com/science/article/pii/S0304406815000336 %0 Journal Article %J Mathematics of Operations Research %D 2015 %T Equimeasurable Rearrangements with Capacities %A M Ghossoub %X

In the classical theory of monotone equimeasurable rearrangements of functions, “equimeasurability” (i.e., that two functions have the same distribution) is defined relative to a given additive probability measure. These rearrangement tools have been successfully used in many problems in economic theory dealing with uncertainty where the monotonicity of a solution is desired. However, in all of these problems, uncertainty refers to the classical Bayesian understanding of the term, where the idea of ambiguity is absent. Arguably, Knightian uncertainty, or ambiguity, is one of the cornerstones of modern decision theory. It is hence natural to seek an extension of these classical tools of equimeasurable rearrangements to the non-Bayesian or neo-Bayesian context. This paper introduces the idea of a monotone equimeasurable rearrangement in the context of nonadditive probabilities, or capacities that satisfy a property that I call strong diffuseness. The latter is a strengthening of the usual notion of diffuseness, and these two properties coincide for additive measures and for submodular (i.e., concave) capacities. To illustrate the usefulness of these tools in economic theory, I consider an application to a problem arising in the theory of production under uncertainty.

%B Mathematics of Operations Research %V 40 %P 429-445 %G eng %U http://pubsonline.informs.org/doi/abs/10.1287/moor.2014.0677 %N 2 %0 Journal Article %J Insurance: Mathematics and Economics %D 2015 %T Vigilant Measures of Risk and the Demand for Contingent Claims %A M Ghossoub %X

We examine a class of utility maximization problems with a non-necessarily law-invariant utility, and with a non-necessarily law-invariant risk measure constraint. Under a consistency requirement on the risk measure that we call Vigilance, we show the existence of optimal contingent claims, and we show that such optimal contingent claims exhibit a desired monotonicity property. Vigilance is satisfied by a large class of risk measures, including all distortion risk measures and some classes of robust risk measures. As an illustration, we consider a problem of optimal insurance design where the premium principle satisfies the vigilance property, hence covering a large collection of commonly used premium principles, including premium principles that are not law-invariant. We show the existence of optimal indemnity schedules, and we show that optimal indemnity schedules are nondecreasing functions of the insurable loss.

%B Insurance: Mathematics and Economics %V 61 %P 27-35 %G eng %U http://www.sciencedirect.com/science/article/pii/S0167668714001619 %N 1 %0 Journal Article %J Mathematics and Financial Economics %D 2010 %T Static Portfolio Choice under Cumulative Prospect Theory %A C Bernard %A M Ghossoub %X

We derive the optimal portfolio choice for an investor who behaves according to Cumulative Prospect Theory (CPT). The study is done in a one-period economy with one risk-free asset and one risky asset, and the reference point corresponds to the terminal wealth arising when the entire initial wealth is invested into the risk-free asset. When it exists, the optimal holding is a function of a generalized Omega measure of the distribution of the excess return on the risky asset over the risk-free rate. It conceptually resembles Merton’s optimal holding for a CRRA expected-utility maximizer. We derive some properties of the optimal holding and illustrate our results using a simple example where the excess return has a skew-normal distribution. In particular, we show how a CPT investor is highly sensitive to the skewness of the excess return on the risky asset. In the model we adopt, with a piecewise-power value function with different shape parameters, loss aversion might be violated for reasons that are now well-understood in the literature. Nevertheless, we argue that this violation is acceptable.

%B Mathematics and Financial Economics %V 2 %P 277-306 %G eng %U https://link.springer.com/article/10.1007%2Fs11579-009-0021-2 %N 4 %0 Book Section %B Debating Globalization: International Perspectives on the Global Economic and Social Order %D 2006 %T On Subsidies, Tariffs, and Wholesale Madness %A Ghossoub, M %B Debating Globalization: International Perspectives on the Global Economic and Social Order %I J.M. Balonze (ed.) - GYAN France, Editions Biliki %P 61-80 %G eng