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Quantitative Finance > Risk Management

arXiv:2108.06940 (q-fin)
[Submitted on 16 Aug 2021 (v1), last revised 2 Aug 2022 (this version, v3)]

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

Authors:Zuo Quan Xu
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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.
Subjects: Risk Management (q-fin.RM); Optimization and Control (math.OC); Probability (math.PR); Mathematical Finance (q-fin.MF)
MSC classes: 91G05,
Cite as: arXiv:2108.06940 [q-fin.RM]
  (or arXiv:2108.06940v3 [q-fin.RM] for this version)
  https://doi.org/10.48550/arXiv.2108.06940
Related DOI: https://doi.org/10.1080/03461238.2022.2092892

Submission history

From: Zuo Quan Xu Dr. [view email]
[v1] Mon, 16 Aug 2021 07:24:11 UTC (17 KB)
[v2] Sun, 19 Jun 2022 13:34:13 UTC (19 KB)
[v3] Tue, 2 Aug 2022 01:25:32 UTC (19 KB)
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