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.
Original language | English |
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Pages (from-to) | 269 - 289 |
Number of pages | 21 |
Journal | Scandinavian Actuarial Journal |
Volume | 2023 |
Issue number | 3 |
DOIs | |
Publication status | Published - Jul 2022 |
Keywords
- Optimal insurance
- mean-variance premium principle
- moral-hazard-free insurance
- quantile optimization
- rank-dependent utility theory
ASJC Scopus subject areas
- Statistics and Probability
- Economics and Econometrics
- Statistics, Probability and Uncertainty