Optimal Insurance Design Under Rank‐Dependent Expected Utility

33 Pages Posted: 17 Jan 2015

See all articles by Carole Bernard

Carole Bernard

Grenoble Ecole de Management; Vrije Universiteit Brussel (VUB)

Xuedong He

Columbia University

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: January 2015

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

Suggested Citation

Bernard, Carole and He, Xuedong and Yan, Jia-an and Zhou, Xun Yu, Optimal Insurance Design Under Rank‐Dependent Expected Utility (January 2015). Mathematical Finance, Vol. 25, Issue 1, pp. 154-186, 2015, Available at SSRN: https://ssrn.com/abstract=2551093 or http://dx.doi.org/10.1111/mafi.12027

Carole Bernard (Contact Author)

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

Xuedong He

Columbia University

3022 Broadway
New York, NY 10027
United States

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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