arXiv subjects

Jean-Gabriel Lauzier

Publications and source records attributed to Jean-Gabriel Lauzier.

8 recordsLinked to original sources

arXiv2026

Optimal risk sharing, equilibria, and welfare with empirically realistic risk attitudes

This paper examines optimal risk sharing. It brings in empirical realism, reckoning with the risk seeking found empirically. We provide results on Pareto optimality, competitive equilibria, utility frontiers, and the first and second theorems of welfare. Empirical studies have found prevailing risk seeking in several subdomains. Thus, as a first step to increase empirical realism, we allow for some risk-seeking agents, still assuming expected utility. Yet more empirical realism is obtained by generalizing expected utility and allowing agents' attitudes to combine risk aversion in some domains with risk seeking in others. We provide results and show directions for future research.

econ.TH↗

arXiv2026

Designing entry-monotone risk-sharing pools

While risk pooling lowers the total cost of risk, efficiency alone does not make a pool viable. Participants need terms that ensure their participation, that are immune to subgroups breaking away, and that allow new members to join. Under cash-additive risk measures, the minimum cost of a coalition's risk determines the value created by that coalition, and deterministic side payments redistribute that value among participants. Institutional risk sharing is thus a transferable-utility cooperative game. We prove that the game is totally balanced whenever the risk measures are convex (agents are risk averse), so every coalition has a nonempty core and stable allocations always exist. We then analyze entry monotonicity through Population-Monotonic Allocation Schemes (Sprumont, 1990), a strong requirement that is notoriously difficult to construct and has received limited attention in risk sharing. We find several structural conditions that ensure that either the Arrow--Debreu pricing surplus allocation rule or the proportional-cost surplus allocation rule satisfies this entry-monotonicity property, the latter being a novel cooperative notion we propose. These verifiable structural conditions naturally arise in pooled (re)insurance and credit portfolios, providing pool designers with a practical toolkit for building risk pools that remain stable and attractive as they expand.

econ.TH↗

arXiv2026

Comonotonic improvement under feasibility constraints

Regulatory and contractual constraints on individual exposures are standard in insurance and reinsurance markets, but a poorly designed constraint can distort the economic incentives of risk-averse agents. In the unconstrained problem, the classical comonotonic improvement theorem guarantees Pareto-optimal allocations that are nondecreasing in the aggregate loss. A constraint that is not stable under risk reduction can destroy this property. We show by example that Value-at-Risk caps lead to optimal allocations that are non-comonotonic in the aggregate loss. We identify componentwise convex-order solidity as a sufficient condition on the feasible set that restores the comonotonic improvement under constraints. If replacing any agent's allocation by a less risky one preserves feasibility, then every feasible allocation admits a feasible comonotonic improvement for all convex-order-consistent preferences. This criterion covers many constraints typical in risk management, but excludes Value-at-Risk caps and idiosyncratic deductibles. We illustrate the implications of our main result in a mean-variance risk-sharing application.

econ.TH↗

arXiv2025

Risk sharing, measuring variability, and distortion riskmetrics

We address the problem of sharing risk among agents with preferences modelled by a general class of comonotonic additive and law-based functionals that need not be either monotone or convex. Such functionals are called distortion riskmetrics, which include many statistical measures of risk and variability used in portfolio optimization and insurance. The set of Pareto-optimal allocations is characterized under various settings of general or comonotonic risk sharing problems. We solve explicitly Pareto-optimal allocations among agents using the Gini deviation, the mean-median deviation, or the inter-quantile difference as the relevant variability measures. The latter is of particular interest, as optimal allocations are not comonotonic in the presence of inter-quantile difference agents; instead, the optimal allocation features a mixture of pairwise counter-monotonic structures, showing some patterns of extremal negative dependence.

q-fin.RM↗

arXiv2023

Pairwise counter-monotonicity

We systematically study pairwise counter-monotonicity, an extremal notion of negative dependence. A stochastic representation and an invariance property are established for this dependence structure. We show that pairwise counter-monotonicity implies negative association, and it is equivalent to joint mix dependence if both are possible for the same marginal distributions. We find an intimate connection between pairwise counter-monotonicity and risk sharing problems for quantile agents. This result highlights the importance of this extremal negative dependence structure in optimal allocations for agents who are not risk averse in the classic sense.

q-fin.RM↗

arXiv2021

Ex-post moral hazard and manipulation-proof contracts

We examine the trade-off between the provision of incentives to exert costly effort (ex-ante moral hazard) and the incentives needed to prevent the agent from manipulating the profit observed by the principal (ex-post moral hazard). Formally, we build a model of two-stage hidden actions where the agent can both influence the expected revenue of a business and manipulate its observed profit. We show that manipulation-proofness is sensitive to the interaction between the manipulation technology and the probability distribution of the stochastic output. The optimal contract is manipulation-proof whenever the manipulation technology is linear. However, a convex manipulation technology sometimes leads to contracts with manipulations in equilibrium. Whenever the distribution satisfies the monotone likelihood ratio property, we can always find a manipulation technology for which the optimal contract is not manipulation-proof.

econ.TH↗

arXiv2021

Envelope theorem and discontinuous optimisation: the case of positioning choice problems

This article examines differentiability properties of the value function of positioning choice problems, a class of optimisation problems in finite-dimensional Euclidean spaces. We show that positioning choice problems' value function is always almost everywhere differentiable even when the objective function is discontinuous. To obtain this result we first show that the Dini superdifferential is always well-defined for the maxima of positioning choice problems. This last property allows to state first-order necessary conditions in terms of Dini supergradients. We then prove our main result, which is an ad-hoc envelope theorem for positioning choice problems. Lastly, after discussing necessity of some key assumptions, we conjecture that similar theorems might hold in other spaces as well.

econ.TH↗

arXiv2021

Insurance design and arson-type risks

We design the insurance contract when the insurer faces arson-type risks. The optimal contract must be manipulation-proof. It is therefore continuous, it has a bounded slope, and it satisfies the no-sabotage condition when arson-type actions are free. Any contract that mixes a deductible, coinsurance and an upper limit is manipulation-proof. We also show that the ability to perform arson-type actions reduces the insured's welfare as less coverage is offered in equilibrium.

econ.TH↗