Optimal Insurance Under Rank‐Dependent Utility and Incentive Compatibility

34 Pages Posted: 13 Mar 2019

See all articles by Zuo Quan Xu

Zuo Quan Xu

The Hong Kong Polytechnic University

Xun Yu Zhou

Columbia University - Department of Industrial Engineering and Operations Research (IEOR)

Sheng Chao Zhuang

University of Nebraska Lincoln

Date Written: April 2019

Abstract

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.

Keywords: incentive compatibility, indemnity function, moral hazard, optimal insurance design, probability weighting function, quantile formulation, rank‐dependent utility theory, retention function

Suggested Citation

Xu, Zuo Quan and Zhou, Xunyu and Zhuang, Sheng Chao, Optimal Insurance Under Rank‐Dependent Utility and Incentive Compatibility (April 2019). Mathematical Finance, Vol. 29, Issue 2, pp. 659-692, 2019, Available at SSRN: https://ssrn.com/abstract=3352081 or http://dx.doi.org/10.1111/mafi.12185

Zuo Quan Xu (Contact Author)

The Hong Kong Polytechnic University ( email )

Xunyu Zhou

Columbia University - Department of Industrial Engineering and Operations Research (IEOR) ( email )

331 S.W. Mudd Building
500 West 120th Street
New York, NY 10027
United States

Sheng Chao Zhuang

University of Nebraska Lincoln ( email )

Lincoln, NE 68588
United States
4024722330 (Phone)

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
0
Abstract Views
356
PlumX Metrics