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

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  • Zuo Quan Xu

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 semi-linear second-order double-obstacle ordinary 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 that is analytically solved.

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  • Zuo Quan Xu, 2023. "Moral-hazard-free insurance: mean-variance premium principle and rank-dependent utility theory," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2023(3), pages 269-289, March.
    • Handle: RePEc:taf:sactxx:v:2023:y:2023:i:3:p:269-289
    DOI: 10.1080/03461238.2022.2092892
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