Optimal Insurance Under Rank-Dependent Expected Utility

33 Pages Posted: 23 Aug 2018 Last revised: 10 Apr 2019

Date Written: April 8, 2019

Abstract

We re-visit the problem of optimal insurance design under Rank-Dependent Expected Utility (RDEU) examined by Bernard et al. (2015), Xu (2018), and Xu et al. (2015). Unlike the latter, we do not impose the no sabotage condition on admissible indemnities, that is, the comonotonicity of indemnity functions and retention functions with the loss. Rather, in a departure from the aforementioned work, we impose a state-verification cost that the insurer can incur in order to verify the loss severity, hence automatically ruling out any ex post moral hazard that could otherwise arise from possible misreporting of the loss by the insured. Hence, monotonicity properties of indemnification schedules become of second-order concern. We fully characterize the optimal indemnity schedule and discuss how our results relate to those of Bernard et al. (2015) and Xu et al. (2015). We then extend the setting by allowing for a distortion premium principle, with a distortion function that differs from that of the insured, and we provide a characterization of the optimal retention in that case.

Keywords: Optimal Insurance, Deductible Contract, Ambiguity, Rank-Dependent Utility, Probability Distortion, Choquet Integral

JEL Classification: C02, D86, G22

Suggested Citation

Ghossoub, Mario, Optimal Insurance Under Rank-Dependent Expected Utility (April 8, 2019). Insurance: Mathematics and Economics, Forthcoming. Available at SSRN: https://ssrn.com/abstract=3230306 or http://dx.doi.org/10.2139/ssrn.3230306

Mario Ghossoub (Contact Author)

University of Waterloo ( email )

Dept. of Statistics & Actuarial Science
200 University Ave. W.
Waterloo, Ontario N2L 3G1
Canada

HOME PAGE: http://uwaterloo.ca/scholar/mghossou

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