Moral-hazard-free insurance: mean-variance premium principle and rank-dependent utility theory. Issue 3 (16th March 2023)

• Record Type: Journal Article
• Authors: Xu, Zuo Quan
• Is Part Of: Scandinavian actuarial journal. Volume 2023:Issue 3(2023)
• Page Start: 269
• Page End: 289
• Publication Date: 2023-03-16
• Subjects: Optimal insurance -- moral-hazard-free insurance -- rank-dependent utility theory -- mean-variance premium principle -- quantile optimization; Insurance, Life -- Mathematics -- Periodicals; Insurance -- Mathematics -- Periodicals; 368.01
• DOI: 10.1080/03461238.2022.2092892
• Languages: English
• ISSNs: 0346-1238

Abstract

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.