@article {36625, title = { The Multiarmed Bandit Problem Under the Mean-Variance Setting }, journal = {European Journal of Operational Research}, year = {Accepted}, author = {Hu, H. and Charpentier, A. and Ghossoub, M. and Schied, A.} } @article {36627, title = { Pareto-Optimal Peer-to-Peer Risk Sharing with Robust Distortion Risk Measures }, journal = {ASTIN~Bulletin}, year = {Accepted}, author = {Ghossoub, M. and Zhu, M.B. and Chong, W.F.} } @article {36626, title = { Risk-Constrained Portfolio Choice under Rank-Dependent Utility }, journal = {Finance and Stochastics}, year = {Accepted}, author = {Ghossoub, M. and Zhu, M.B.} } @article {36624, title = { Bowley-Optimal Convex-Loaded Premium Principles }, journal = {Insurance: Mathematics and Economics}, volume = {121}, year = {2025}, pages = {157-180}, author = {Ghossoub, M. and Li, B. and Shi, B.} } @article {36623, title = { Comonotonicity and Pareto Optimality, with Application to Collaborative Insurance }, journal = {Insurance: Mathematics and Economics}, volume = {120}, year = {2025}, pages = {1-16}, author = {Denuit, M. and Dhaene, J., and Ghossoub, M. and Robert, C.} } @article {33082, title = {Bounds on Choquet Risk Measures in Finite Product Spaces with Ambiguous Marginals}, journal = {Statistics \& Risk Modeling}, volume = {41}, year = {2024}, pages = {49-72}, author = {Ghossoub, M. and Saunders, D. and Zhang, K.S.} } @article {32334, title = {(No-)Betting Pareto Optima under Rank-Dependent Utility}, journal = {Mathematics of Operations Research}, volume = {49}, year = {2024}, pages = {1452-1471}, author = {Beissner, P. and Boonen, T. and Ghossoub, M.} } @article {34907, title = {Pareto-Efficient Risk Sharing in Centralized Insurance Markets with Application to Flood Risk}, journal = {Journal of Risk and Insurance}, volume = {91}, year = {2024}, pages = {449-488}, author = {T.J. Boonen and A. Chong} } @article {32346, title = {Pareto-Optimal Insurance with an Upper Limit on the Insurer\&$\#$39;s Exposure}, journal = {Scandinavian Actuarial Journal}, volume = {2024}, year = {2024}, pages = {227-251}, author = {Coke, O and Ghossoub, M and Zhu, M} } @article {34901, title = {Stackelberg Equilibria with Multiple Policyholders}, journal = {Insurance: Mathematics and Economics}, volume = {116}, year = {2024}, pages = {189-201}, author = {Ghossoub, M. and Zhu, M.B.} } @article {31340, title = {Bowley vs. Pareto Optima in Reinsurance Contracting}, journal = {European Journal of Operational Research}, volume = {307}, year = {2023}, pages = {382-391}, url = {https://www.sciencedirect.com/science/article/abs/pii/S0377221722006476?via\%3Dihub}, author = {Boonen, T.J. and Ghossoub, M.} } @article {32366, title = {Equilibria and Efficiency in a Reinsurance Market}, journal = {Insurance: Mathematics and Economics}, volume = {113}, year = {2023}, pages = {24-49}, author = {Zhu, M.B. and Ghossoub, M. and Boonen, T.J.} } @article {31048, title = {Maximum Spectral Measures of Risk with given Risk Factor Marginal Distributions}, journal = {Mathematics of Operations Research}, volume = {48}, year = {2023}, pages = {1158-1182}, author = {Mario Ghossoub and Jesse Hall and David Saunders} } @article {31431, title = {Optimal Insurance for a Prudent Decision-Maker under Heterogeneous Beliefs}, journal = {European Actuarial Journal}, volume = {13}, year = {2023}, pages = {703-730}, author = {Ghossoub, M. and Jiang, W. and Ren, J.} } @article {32117, title = {Optimal Insurance under Maxmin-Expected-Utility}, journal = {Finance and Stochastics}, volume = {27}, year = {2023}, pages = {467-501}, url = {https://link.springer.com/article/10.1007/s00780-023-00497-y}, author = {Birghila, C. and Boonen, T.J. and Ghossoub, M.} } @article {31299, title = {Pareto-Optimal Reinsurance under Individual Risk Constraints}, journal = {Insurance: Mathematics and Economics}, volume = {107}, year = {2022}, pages = {307-325}, author = {Ghossoub, M. and Jiang, W. and Ren, J.} } @article {28890, title = {Aggregation of Opinions and Risk Measures}, journal = {Journal of Economic Theory}, volume = {196}, year = {2021}, url = {https://www.sciencedirect.com/science/article/abs/pii/S0022053121001277}, author = {Massimiliano Amarante and Mario Ghossoub} } @article {24820, title = {Comparative Risk Aversion in RDEU with Applications to Optimal Underwriting of Securities Issuance}, journal = {Insurance: Mathematics and Economics}, volume = {101}, year = {2021}, pages = {6-22}, url = {https://www.sciencedirect.com/science/article/abs/pii/S0167668720300871}, author = {Mario Ghossoub and Xuedong He} } @article {26337, title = {On the Continuity of the Feasible Set Mapping in Optimal Transport}, journal = {Economic Theory Bulletin}, year = {2021}, url = {https://link.springer.com/article/10.1007/s40505-021-00199-8}, author = {M. Ghossoub and D. Saunders} } @article {24819, title = {Optimal Reinsurance with Multiple Reinsurers: Distortion Risk Measures, Distortion Premium Principles, and Heterogeneous Beliefs}, journal = {Insurance: Mathematics and Economics}, volume = {101}, year = {2021}, pages = {23-37}, url = {https://www.sciencedirect.com/science/article/abs/pii/S0167668720300883}, author = {Tim Boonen and Mario Ghossoub} } @article {23462, title = {Bilateral Risk Sharing with Heterogeneous Beliefs and Exposure Constraints}, journal = {ASTIN Bulletin}, volume = {50}, year = {2020}, pages = {293-323}, url = {https://www.cambridge.org/core/journals/astin-bulletin-journal-of-the-iaa/article/bilateral-risk-sharing-with-heterogeneous-beliefs-and-exposure-constraints/96919FC90D5D9091B1592464720A1E16}, author = {Tim Boonen and Mario Ghossoub} } @article {18694, title = {Budget-Constrained Optimal Retention With an Upper Limit on the Retained Loss}, journal = {Scandinavian Actuarial Journal}, volume = {2020}, year = {2020}, pages = {245-271}, url = {https://www.tandfonline.com/doi/full/10.1080/03461238.2019.1659177}, author = {Mario Ghossoub} } @article {20995, title = {Budget-Constrained Optimal Insurance with Belief Heterogeneity}, journal = {Insurance: Mathematics and Economics}, volume = {89}, year = {2019}, pages = {79-91}, url = {https://www.sciencedirect.com/science/article/pii/S0167668719303907} } @article {15104, title = {Budget-Constrained Optimal Insurance Without the Nonnegativity Constraint on Indemnities}, journal = {Insurance: Mathematics and Economics}, volume = {84}, year = {2019}, month = {Jan 2019}, pages = {22-39}, url = {https://www.sciencedirect.com/science/article/pii/S016766871730389X?via\%3Dihub}, author = {Mario Ghossoub} } @article {18575, title = {On the Existence of a Representative Reinsurer under Heterogeneous Beliefs}, journal = {Insurance: Mathematics and Economics}, volume = {88}, year = {2019}, pages = {209-225}, url = {https://www.sciencedirect.com/science/article/pii/S0167668718305365}, author = {Tim Boonen and Mario Ghossoub} } @article {16651, title = {Optimal Insurance under Rank-Dependent Expected Utility}, journal = {Insurance: Mathematics and Economics}, volume = {87}, year = {2019}, pages = {51-66}, url = {https://www.sciencedirect.com/science/article/pii/S0167668718302531?via\%3Dihub}, author = {Mario Ghossoub} } @article {7420, title = {A Neyman-Pearson Problem with Ambiguity and Nonlinear Pricing}, journal = {Mathematics and Financial Economics}, volume = {12}, year = {2018}, pages = {365-385}, abstract = {

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.

}, url = {https://link.springer.com/article/10.1007\%2Fs11579-017-0207-y}, author = {Ghossoub, M.} } @article {Ghossoub2017, title = {Arrow\&$\#$39;s Theorem of the Deducible with Heterogeneous Beliefs}, journal = {North American Actuarial Journal}, volume = {21}, number = {1}, year = {2017}, pages = {15-35}, abstract = {

In Arrow{\textquoteright}s classical problem of demand for insurance indemnity schedules, it is well-known that the optimal insurance indemnification for an insurance buyer{\textemdash}or decision maker (DM){\textemdash}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{\textquoteright}s framework, however, both parties share the same probabilistic beliefs about the realizations of the underlying insurable loss. This article reexamines Arrow{\textquoteright}s problem in a setting where the DM and the insurer have different subjective beliefs. Under a requirement of compatibility between the insurer{\textquoteright}s and the DM{\textquoteright}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{\textquoteright}s classical result is then obtained as a special case.

}, url = {http://www.tandfonline.com/doi/full/10.1080/10920277.2016.1192477}, author = {M Ghossoub} } @article {AGP2016, title = {Contracting on Ambiguous Prospects}, journal = {Economic Journal}, volume = {127}, year = {2017}, pages = {2241-2262}, abstract = {

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{\textquoteright}s attitude towards ambiguity. Sharper results obtain in the case of global ambiguity-loving behaviour.

}, url = {http://onlinelibrary.wiley.com/doi/10.1111/ecoj.12381/abstract}, author = {M. Amarante and M. Ghossoub and E.S Phelps} } @article {Ghossoub2016MFE, title = {Cost-Efficient Contingent Claims with Market Frictions}, journal = {Mathematics and Financial Economics}, volume = {10}, number = {1}, year = {2016}, pages = {87-111}, abstract = {

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{\textquoteright}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 {\textquotedblleft}law-invariant{\textquotedblright} 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{\textquoteright}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.

}, url = {https://link.springer.com/article/10.1007/s11579-015-0151-7}, author = {M Ghossoub} } @article {AmaranteGhossoub2016, title = {Optimal Insurance for a Minimal Expected Retention: The Case of an Ambiguity-Seeking Insurer}, journal = {Risks}, volume = {4}, number = {1}, year = {2016}, pages = {8}, abstract = {

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{\textquoteright}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{\textquoteright}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.

}, url = {http://www.mdpi.com/2227-9091/4/1/8}, author = {M. Amarante and M Ghossoub} } @article {Ghossoub2015b, title = {Optimal Insurance with Heterogeneous Beliefs and Disagreement about Zero-Probability Events}, journal = {Risks}, volume = {4}, number = {3}, year = {2016}, pages = {29}, abstract = {

In problems of optimal insurance design, Arrow{\textquoteright}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{\textquoteright}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{\textquoteright}s probability measure, and we obtain Arrow{\textquoteright}s classical result, as well as one of the results of Ghossoub as corollaries. Finally, we formalize Marshall{\textquoteright}s argument that, in a setting of belief heterogeneity, an optimal indemnity schedule may take {\textquotedblleft}any{\textquotedblright}shape.

}, url = {http://www.mdpi.com/2227-9091/4/3/29}, author = {M Ghossoub} } @article {AGP2015, title = {Ambiguity on the Insurer\&$\#$39;s Side: The Demand for Insurance}, journal = {Journal of Mathematical Economics}, volume = {58}, year = {2015}, pages = {61-78}, abstract = {

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.

}, url = {http://www.sciencedirect.com/science/article/pii/S0304406815000336}, author = {M. Amarante and M. Ghossoub and E.S Phelps} } @article {Ghossoub2015MOR, title = {Equimeasurable Rearrangements with Capacities}, journal = {Mathematics of Operations Research}, volume = {40}, number = {2}, year = {2015}, pages = {429-445}, abstract = {

In the classical theory of\ monotone equimeasurable rearrangements\ of functions, {\textquotedblleft}equimeasurability{\textquotedblright} (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.

}, url = {http://pubsonline.informs.org/doi/abs/10.1287/moor.2014.0677}, author = {M Ghossoub} } @article {Ghossoub2015a, title = {Vigilant Measures of Risk and the Demand for Contingent Claims}, journal = {Insurance: Mathematics and Economics}, volume = {61}, year = {2015}, pages = {27-35}, abstract = {

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.

}, url = {http://www.sciencedirect.com/science/article/pii/S0167668714001619}, author = {M Ghossoub} } @article {BernardGhossoub2010, title = {Static Portfolio Choice under Cumulative Prospect Theory}, journal = {Mathematics and Financial Economics}, volume = {2}, number = {4}, year = {2010}, pages = {277-306}, abstract = {

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{\textquoteright}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.

}, url = {https://link.springer.com/article/10.1007\%2Fs11579-009-0021-2}, author = {C Bernard and M Ghossoub} } @inbook {6109, title = {On Subsidies, Tariffs, and Wholesale Madness}, booktitle = {Debating Globalization: International Perspectives on the Global Economic and Social Order}, year = {2006}, pages = {61-80}, publisher = {J.M. Balonze (ed.) - GYAN France, Editions Biliki}, organization = {J.M. Balonze (ed.) - GYAN France, Editions Biliki}, author = {Ghossoub, M} }