arXiv subjects

Mario Ghossoub

Publications and source records attributed to Mario Ghossoub.

18 recordsLinked to original sources

arXiv2026

Dynamic Pareto Optima in Multi-Period Pure-Exchange Economies

We study a problem of optimal allocation in a discrete-time multi-period pure-exchange economy, where agents have preferences over stochastic endowment processes that are represented by strongly time-consistent dynamic risk measures. We introduce the notion of dynamic Pareto-optimal allocation processes and show that such processes can be constructed recursively starting with the allocation at the terminal time. We further derive a comonotone improvement theorem for allocation processes, and we provide a recursive approach to constructing comonotone dynamic Pareto optima when the agents' preferences are coherent and satisfy a property that we call equidistribution-preserving. In the special case where each agent's dynamic risk measure is of the distortion type, we provide a closed-form characterization of comonotone dynamic Pareto optima. We illustrate our results in a two-period setting.

q-fin.RM↗

arXiv2026

Betting under Common Beliefs: The Effect of Probability Weighting

This paper examines the impact of introducing a Rank-Dependent Utility (RDU) agent into a von Neumann-Morgenstern (vNM) pure-exchange economy with no aggregate uncertainty. In the absence of the RDU agent, the classical theory predicts that Pareto-optimal allocations are full-insurance, or no-betting, allocations. We show how the probability weighting function of the RDU agent, seen as a proxy for probabilistic risk aversion that is not captured by marginal utility of wealth, can lead to Pareto optima characterized by endogenous betting, despite common baseline beliefs. Such endogenous betting at an optimum leads to uncertainty-generating trade arising purely from heterogeneity in the perception of risk, rather than in beliefs. Our results formalize the intuitive understanding that probability weighting can act as an endogenous source of belief heterogeneity, and provide a new behavioral foundation for the coexistence of common beliefs and speculative behavior, in an environment with no initial aggregate uncertainty. Interpreting the RDU agent's nonlinear weighting function as an ``internality'' prompts the question of whether a social planner should intervene. We show how a benevolent social planner can nudge the RDU agent to behave closer to a vNM agent, through costly statistical or financial education, thereby (partially) restoring the optimality of full-insurance allocations.

econ.TH↗

arXiv2026

Stackelberg Equilibria in Monopoly Insurance Markets with Probability Weighting

We study Stackelberg Equilibria (Bowley optima) in a monopolistic centralized sequential-move insurance market, with a profit-maximizing insurer who sets premia using a distortion premium principle, and a single policyholder who seeks to minimize a distortion risk measure. We show that equilibria are characterized as follows: In equilibrium, the optimal indemnity function exhibits a layer-type structure, providing full insurance over any loss layer on which the policyholder is more pessimistic than the insurer's pricing functional about tail losses; and no insurance coverage over loss layers on which the policyholder is less pessimistic than the insurer's pricing functional about tail losses. In equilibrium, the optimal pricing distortion function is determined by the policyholder's degree of risk aversion, whereby prices never exceed the policyholder's marginal willingness to insure tail losses. Moreover, we show that both the insurance coverage and the insurer's expected profit increase with the policyholder's degree of risk aversion. Additionally, and echoing recent work in the literature, we show that equilibrium contracts are Pareto efficient, but they do not induce a welfare gain to the policyholder. Conversely, any Pareto-optimal contract that leaves no welfare gain to the policyholder can be obtained as an equilibrium contract. Finally, we consider a few examples of interest that recover some existing results in the literature as special cases of our analysis.

q-fin.RM↗

arXiv2026

Incentive Pareto Efficiency in Monopoly Insurance Markets with Adverse Selection

We study a monopolistic insurance market with hidden information, where the agent's type $\theta$ is private information that is unobservable to the insurer, and it is drawn from a continuum of types. The hidden type affects both the loss distribution and the risk attitude of the agent. Within this framework, we show that a menu of contracts is incentive efficient if it maximizes social welfare function, subject to incentive compatibility and individual rationality constraints. This holds for general utility functionals. In the special case of Yaari Dual Utility, we provide two partial converse statements to this result, and we give a semi-explicit characterization of optimal solutions to the social welfare maximization problem. We do this under two different settings: (i) the first assumes that types are ordered in a way such that larger values of $\theta$ correspond to more risk-averse types who face stochastically larger losses; whereas (ii) the second assumes that larger values of $\theta$ correspond to less risk-averse types who face stochastically larger losses. In both settings, the structure of optimal menus of contracts depends on the level of the social welfare weight, and we examine several properties thereof.

econ.TH↗

arXiv2025

Optimal allocations with distortion risk measures and mixed risk attitudes

We study Pareto-optimal risk sharing in economies with heterogeneous attitudes toward risk, where agents' preferences are modeled by distortion risk measures. Building on comonotonic and counter-monotonic improvement results, we show that agents with similar attitudes optimally share risks comonotonically (risk-averse) or counter-monotonically (risk-seeking). We show how the general $n$-agent problem can be reduced to a two-agent formulation between representative risk-averse and risk-seeking agents, characterized by the infimal convolution of their distortion risk measures. Within this two-agent framework, we establish necessary and sufficient conditions for the existence of optimal allocations, and we identify when the infimal convolution yields an unbounded value. When existence fails, we analyze the problem under nonnegative allocation constraints, and we characterize optima explicitly, under piecewise-linear distortion functions and Bernoulli-type risks. Our findings suggest that the optimal allocation structure is governed by the relative strength of risk aversion versus risk seeking behavior, as intuition would suggest.

econ.TH↗

arXiv2025

Subgame Perfect Nash Equilibria in Large Reinsurance Markets

We consider a model of a reinsurance market consisting of multiple insurers on the demand side and multiple reinsurers on the supply side, thereby providing a unifying framework and extension of the recent literature on optimality and equilibria in reinsurance markets. Each insurer has preferences represented by a general Choquet risk measure and can purchase coverage from any or all reinsurers. Each reinsurer has preferences represented by a general Choquet risk measure and can provide coverage to any or all insurers. Pricing in this market is done via a nonlinear pricing rule given by a Choquet integral. We model the market as a sequential game in which the reinsurers have the first-move advantage. We characterize the Subgame Perfect Nash Equilibria in this market in some cases of interest, and we examine their Pareto efficiency. In addition, we consider two special cases of our model that correspond to existing models in the related literature, and we show how our findings extend these previous results. Finally, we illustrate our results in a numerical example.

q-fin.RM↗

arXiv2025

Optimal Insurance in a Monopoly: Dual Utilities with Hidden Risk Attitudes

We consider a monopoly insurance market with a risk-neutral profit-maximizing insurer and a consumer with Yaari Dual Utility preferences that distort the given continuous loss distribution. The insurer observes the loss distribution but not the risk attitude of the consumer, proxied by a distortion function drawn from a continuum of types. We characterize the profit-maximizing, incentive-compatible, and individually rational menus of insurance contracts, show that equilibria are separating, and provide key properties thereof. Notably, insurance coverage and premia are monotone in the level of risk aversion; the most risk-averse consumer receives full insurance $(\textit{efficiency at the top})$; the monopoly absorbs all surplus from the least-risk averse consumer; and consumers with a higher level of risk aversion induce a higher expected profit for the insurer. Under certain regularity conditions, equilibrium contracts can be characterized in terms of the marginal loss retention per type of consumer, and they consist of menus of layered deductible contracts, where each such layered structure is determined by the risk type of the consumer. In addition, we examine the effect of a fixed insurance provision cost on equilibria. We show that if the fixed cost is prohibitively high, then there will be no $\textit{ex ante}$ gains from trade. However, when trade occurs, separating equilibrium contracts always outperform pooling equilibrium contracts, and they are identical to those obtained in the absence of fixed costs, with the exception that only part of the menu is excluded. The excluded contracts are those designed for consumers with relatively lower risk aversion, who are less valuable to the insurer. Finally, we characterize incentive-efficient menus of contracts in the context of an arbitrary type space.

econ.TH↗

arXiv2024

Counter-monotonic Risk Sharing with Heterogeneous Distortion Risk Measures

We study risk sharing among agents with preferences modeled by heterogeneous distortion risk measures, who are not necessarily risk averse. Pareto optimality for agents using risk measures is often studied through the lens of inf-convolutions, because allocations that attain the inf-convolution are Pareto optimal, and the converse holds true under translation invariance. Our main focus is on groups of agents who exhibit varying levels of risk seeking. Under mild assumptions, we derive explicit solutions for the unconstrained inf-convolution and the counter-monotonic inf-convolution, which can be represented by a generalization of distortion risk measures.

q-fin.RM↗

arXiv2024

Pareto-Optimal Peer-to-Peer Risk Sharing with Robust Distortion Risk Measures

We study Pareto optimality in a decentralized peer-to-peer risk-sharing market where agents' preferences are represented by robust distortion risk measures that are not necessarily convex. We obtain a characterization of Pareto-optimal allocations of the aggregate risk in the market, and we show that the shape of the allocations depends primarily on each agent's assessment of the tail of the aggregate risk. We quantify the latter via an index of probabilistic risk aversion, and we illustrate our results using concrete examples of popular families of distortion functions. As an application of our results, we revisit the market for flood risk insurance in the United States. We present the decentralized risk sharing arrangement as an alternative to the current centralized market structure, and we characterize the optimal allocations in a numerical study with historical flood data. We conclude with an in-depth discussion of the advantages and disadvantages of a decentralized insurance scheme in this setting.

q-fin.RM↗

arXiv2024

Counter-monotonic risk allocations and distortion risk measures

In risk-sharing markets with aggregate uncertainty, characterizing Pareto-optimal allocations when agents might not be risk averse is a challenging task, and the literature has only provided limited explicit results thus far. In particular, Pareto optima in such a setting may not necessarily be comonotonic, in contrast to the case of risk-averse agents. In fact, when market participants are risk-seeking, Pareto-optimal allocations are counter-monotonic. Counter-monotonicity of Pareto optima also arises in some situations for quantile-optimizing agents. In this paper, we provide a systematic study of efficient risk sharing in markets where allocations are constrained to be counter-monotonic. The preferences of the agents are modelled by a common distortion risk measure, or equivalently, by a common Yaari dual utility. We consider three different settings: risk-averse agents, risk-seeking agents, and those with an inverse S-shaped distortion function. In each case, we provide useful characterizations of optimal allocations, for both the counter-monotonic market and the unconstrained market. To illustrate our results, we consider an application to a portfolio choice problem for a portfolio manager tasked with managing the investments of a group of clients, with varying levels of risk aversion or risk seeking. We determine explicitly the optimal investment strategies in this case. Our results confirm the intuition that a manager investing on behalf of risk-seeking agents tends to invest more in risky assets than a manager acting on behalf of risk-averse agents.

q-fin.RM↗

arXiv2024

Efficiency in Pure-Exchange Economies with Risk-Averse Monetary Utilities

We study Pareto efficiency in a pure-exchange economy where agents' preferences are represented by risk-averse monetary utilities. These coincide with law-invariant monetary utilities, and they can be shown to correspond to the class of monotone, (quasi-)concave, Schur concave, and translation-invariant utility functionals. This covers a large class of utility functionals, including a variety of law-invariant robust utilities. We show that Pareto optima exist and are comonotone, and we provide a crisp characterization thereof in the case of law-invariant positively homogeneous monetary utilities. This characterization provides an easily implementable algorithm that fully determines the shape of Pareto-optimal allocations. In the special case of law-invariant comonotone-additive monetary utility functionals (concave Yaari-Dual utilities), we provide a closed-form characterization of Pareto optima. As an application, we examine risk-sharing markets where all agents evaluate risk through law-invariant coherent risk measures, a widely popular class of risk measures. In a numerical illustration, we characterize Pareto-optimal risk-sharing for some special types of coherent risk measures.

q-fin.MF↗

arXiv2024

Allocation Mechanisms in Decentralized Exchange Markets with Frictions

The classical theory of efficient allocations of an aggregate endowment in a pure-exchange economy has hitherto primarily focused on the Pareto-efficiency of allocations, under the implicit assumption that transfers between agents are frictionless, and hence costless to the economy. In this paper, we argue that certain transfers cause frictions that result in costs to the economy. We show that these frictional costs are tantamount to a form of subadditivity of the cost of transferring endowments between agents. We suggest an axiomatic study of allocation mechanisms, that is, the mechanisms that transform feasible allocations into other feasible allocations, in the presence of such transfer costs. Among other results, we provide an axiomatic characterization of those allocation mechanisms that admit representations as robust (worst-case) linear allocation mechanisms, as well as those mechanisms that admit representations as worst-case conditional expectations. We call the latter Robust Conditional Mean Allocation mechanisms, and we relate our results to the literature on (decentralized) risk sharing within a pool of agents.

cs.GT↗

arXiv2023

A Nonlinear Sandwich Theorem

We provide a Sandwich Theorem (K\"onig (1972)) for positively homogeneous functionals that satisfy additivity only on a restricted domain. Our relaxation of additivity is based on a binary relation called convex-conic symmetric preorder, whereby additivity is restricted to all couples of elements that belong to such relation. We then study applications of our nonlinear Sandwich Theorem, proving extension and envelope representation results. Finally, we consider some applications to comonotonicity, a key property in decision theory, risk measurement, and the theory of risk sharing.

math.FA↗

arXiv2022

Multiarmed Bandits Problem Under the Mean-Variance Setting

The classical multi-armed bandit (MAB) problem involves a learner and a collection of K independent arms, each with its own ex ante unknown independent reward distribution. At each one of a finite number of rounds, the learner selects one arm and receives new information. The learner often faces an exploration-exploitation dilemma: exploiting the current information by playing the arm with the highest estimated reward versus exploring all arms to gather more reward information. The design objective aims to maximize the expected cumulative reward over all rounds. However, such an objective does not account for a risk-reward tradeoff, which is often a fundamental precept in many areas of applications, most notably in finance and economics. In this paper, we build upon Sani et al. (2012) and extend the classical MAB problem to a mean-variance setting. Specifically, we relax the assumptions of independent arms and bounded rewards made in Sani et al. (2012) by considering sub-Gaussian arms. We introduce the Risk Aware Lower Confidence Bound (RALCB) algorithm to solve the problem, and study some of its properties. Finally, we perform a number of numerical simulations to demonstrate that, in both independent and dependent scenarios, our suggested approach performs better than the algorithm suggested by Sani et al. (2012).

math.OC↗

arXiv2022

Bounds on Choquet Risk Measures in Finite Product Spaces with Ambiguous Marginals

We investigate the problem of finding upper and lower bounds for a Choquet risk measure of a nonlinear function of two risk factors, when the marginal distributions of the risk factors are ambiguous and represented by nonadditive measures on the marginal spaces and the joint nonadditive distribution on the product space is unknown. We treat this problem as a generalization of the optimal transport problem to the setting of nonadditive measures. We provide explicit characterizations of the optimal solutions for finite marginal spaces, and we investigate some of their properties. We further discuss the connections with linear programming, showing that the optimal transport problems for capacities are linear programs, and we also characterize their duals explicitly. Finally, we investigate a series of numerical examples, including a comparison with the classical optimal transport problem, and applications to counterparty credit risk.

math.PR↗

arXiv2020

Maximum Spectral Measures of Risk with given Risk Factor Marginal Distributions

We consider the problem of determining an upper bound for the value of a spectral risk measure of a loss that is a general nonlinear function of two factors whose marginal distributions are known, but whose joint distribution is unknown. The factors may take values in complete separable metric spaces. We introduce the notion of Maximum Spectral Measure (MSP), as a worst-case spectral risk measure of the loss with respect to the dependence between the factors. The MSP admits a formulation as a solution to an optimization problem that has the same constraint set as the optimal transport problem, but with a more general objective function. We present results analogous to the Kantorovich duality, and we investigate the continuity properties of the optimal value function and optimal solution set with respect to perturbation of the marginal distributions. Additionally, we provide an asymptotic result characterizing the limiting distribution of the optimal value function when the factor distributions are simulated from finite sample spaces. The special case of Expected Shortfall and the resulting Maximum Expected Shortfall is also examined.

q-fin.RM↗

arXiv2020

Optimal Insurance under Maxmin Expected Utility

We examine a problem of demand for insurance indemnification, when the insured is sensitive to ambiguity and behaves according to the Maxmin-Expected Utility model of Gilboa and Schmeidler (1989), whereas the insurer is a (risk-averse or risk-neutral) Expected-Utility maximizer. We characterize optimal indemnity functions both with and without the customary ex ante no-sabotage requirement on feasible indemnities, and for both concave and linear utility functions for the two agents. This allows us to provide a unifying framework in which we examine the effects of the no-sabotage condition, marginal utility of wealth, belief heterogeneity, as well as ambiguity (multiplicity of priors) on the structure of optimal indemnity functions. In particular, we show how the singularity in beliefs leads to an optimal indemnity function that involves full insurance on an event to which the insurer assigns zero probability, while the decision maker assigns a positive probability. We examine several illustrative examples, and we provide numerical studies for the case of a Wasserstein and a Renyi ambiguity set.

q-fin.RM↗

arXiv2020

On the Continuity of the Feasible Set Mapping in Optimal Transport

Consider the set of probability measures with given marginal distributions on the product of two complete, separable metric spaces, seen as a correspondence when the marginal distributions vary. In problems of optimal transport, continuity of this correspondence from marginal to joint distributions is often desired, in light of Berge's Maximum Theorem, to establish continuity of the value function in the marginal distributions, as well as stability of the set of optimal transport plans. Bergin (1999) established the continuity of this correspondence, and in this note, we present a novel and considerably shorter proof of this important result. We then examine an application to an assignment game (transferable utility matching problem) with unknown type distributions.

q-fin.RM↗