Moral-hazard-free insurance: mean-variance premium principle and rank-dependent utility theory

Zuo Quan Xu

Papers from arXiv.org

Abstract: This paper investigates a Pareto optimal insurance problem, where the insured maximizes her rank-dependent utility preference and the insurer is risk neutral and employs the mean-variance premium principle. To eliminate potential moral hazard issues, we only consider the so-called moral-hazard-free insurance contracts that obey the incentive compatibility constraint. The insurance problem is first formulated as a non-concave maximization problem involving Choquet expectation, then turned into a concave quantile optimization problem and finally solved by the calculus of variations method. The optimal contract is expressed by a second-order ordinary integro-differential equation with nonlocal operator. An effective numerical method is proposed to compute the optimal contract assuming the probability weighting function has a density. Also, we provide an example which is analytically solved.

Date: 2021-08, Revised 2022-08
New Economics Papers: this item is included in nep-cta, nep-ias, nep-isf and nep-upt
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