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

Zuo Quan Xu

Scandinavian Actuarial Journal, 2023, vol. 2023, issue 3, 269-289

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.

Date: 2023
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DOI: 10.1080/03461238.2022.2092892

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