Optimal insurance under rank-dependent utility and incentive compatibility. (English) Zbl 1411.91325

Xu, Zuo Quan; Zhou, Xun Yu; Zhuang, Sheng Chao

Math. Finance 29, No. 2, 659-692 (2019).

Summary: Bernard, He, Yan, and Zhou (Mathematical Finance, 25(1), 154–186) studied an optimal insurance design problem where an individual’s preference is of the rank-dependent utility (RDU) type, and show that in general an optimal contract covers both large and small losses. However, their results suffer from the unrealistic assumption that the random loss has no atom, as well as a problem of moral hazard that provides incentives for the insured to falsely report the actual loss. This paper addresses these setbacks by removing the nonatomic assumption, and by exogenously imposing the “incentive compatibility” constraint that both indemnity function and insured’s retention function are increasing with respect to the loss. We characterize the optimal solutions via calculus of variations, and then apply the result to obtain explicitly expressed contracts for problems with Yaari’s dual criterion and general RDU. Finally, we use numerical examples to compare the results between ours and Bernard et al.

MSC:

91B30	Risk theory, insurance (MSC2010)
91B16	Utility theory

Keywords:

incentive compatibility; indemnity function; moral hazard; optimal insurance design; probability weighting function; quantile formulation; rank-dependent utility theory; retention function