Optimal Insurance with Rank-Dependent Utility and Increasing Indemnities

33 Pages Posted: 15 Sep 2015

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: September 8, 2015

Abstract

Bernard et al. (2015) study 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 contracts suffer from a problem of moral hazard for paying more compensation for a smaller loss. This paper addresses this setback by exogenously imposing the constraint that both the indemnity function and the insured’s retention function be 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 a numerical example to compare the results between ours and that of Bernard et al. (2015).

Keywords: optimal insurance design, rank-dependent utility theory, Yaari’s dual criterion, probability weighting function, moral hazard, indemnity function, retention function, quantile formulation

JEL Classification: G22, D81, D82

Suggested Citation

Xu, Zuo Quan and Zhou, Xunyu and Zhuang, Sheng Chao, Optimal Insurance with Rank-Dependent Utility and Increasing Indemnities (September 8, 2015). Available at SSRN: https://ssrn.com/abstract=2660113 or http://dx.doi.org/10.2139/ssrn.2660113

Zuo Quan Xu

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 (Contact Author)

University of Nebraska Lincoln ( email )

Lincoln, NE 68588
United States
4024722330 (Phone)

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