Optimal Insurance Design Under Rank-Dependent Expected Utility

42 Pages Posted: 11 Jul 2011 Last revised: 11 Dec 2012

See all articles by Carole Bernard

Carole Bernard

Grenoble Ecole de Management; Vrije Universiteit Brussel (VUB)

Xue Dong He

The Chinese University of Hong Kong - Department of Systems Engineering and Engineering Management

Jia‐An Yan

Chinese Academy of Sciences (CAS) - Academy of Mathematics and Systems Sciences

Xun Yu Zhou

The Chinese University of Hong Kong (CUHK) - Department of Systems Engineering & Engineering Management

Multiple version iconThere are 2 versions of this paper

Date Written: October 9, 2012

Abstract

We consider an optimal insurance design problem for an individual whose preferences are dictated by the rank-dependent expected utility (RDEU) theory with a concave utility function and an inverse-S shaped probability distortion function. This type of RDEU is known to describe human behavior better than the classical expected utility. By applying the technique of quantile formulation, we solve the problem explicitly. We show that the optimal contract not only insures large losses above a deductible but also insures small losses fully. This is consistent, for instance, with the demand for warranties. Finally, we compare our results, analytically and numerically, both to those in the expected utility framework and to cases in which the distortion function is convex or concave.

Keywords: optimal insurance design, rank-dependent expected utility, inverse-S shaped probability distortion, indemnity, quantile formulation, deductible

JEL Classification: G22, D81, D82

Suggested Citation

Bernard, Carole and He, Xue Dong and Yan, Jia-an and Zhou, Xun Yu, Optimal Insurance Design Under Rank-Dependent Expected Utility (October 9, 2012). Available at SSRN: https://ssrn.com/abstract=1883519 or http://dx.doi.org/10.2139/ssrn.1883519

Carole Bernard

Grenoble Ecole de Management ( email )

12, rue Pierre Sémard
Grenoble Cedex, 38003
France

Vrije Universiteit Brussel (VUB) ( email )

Pleinlaan 2
http://www.vub.ac.be/
Brussels, 1050
Belgium

Xue Dong He (Contact Author)

The Chinese University of Hong Kong - Department of Systems Engineering and Engineering Management ( email )

505 William M.W. Mong Engineering Building
The Chinese University of Hong Kong, Shatin, N.T.
Hong Kong
Hong Kong

HOME PAGE: http://https://sites.google.com/site/xuedonghepage/home

Jia-an Yan

Chinese Academy of Sciences (CAS) - Academy of Mathematics and Systems Sciences ( email )

Zhong-Guan-Cun-Dong-Lu 55
Beijing, 100190
China

Xun Yu Zhou

The Chinese University of Hong Kong (CUHK) - Department of Systems Engineering & Engineering Management ( email )

Shatin, New Territories
Hong Kong
852 2609-8320 (Phone)
852 2603-5505 (Fax)

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