Optimal Insurance for a Minimal Expected Retention: The Case of an Ambiguity-Seeking Insurer

Risks, 4(1):8, 2016

33 Pages Posted: 30 Jan 2015 Last revised: 16 Mar 2017

Date Written: January 27, 2015

Abstract

In the classical Expected-Utility framework, a problem of optimal insurance design with a premium constraint is equivalent to a problem of optimal insurance design with a minimum expected retention constraint. When the insurer has ambiguous beliefs represented by a non-additive probability measure, as in Schmeidler (1989), this equivalence no longer holds. A problem of optimal insurance design with a premium constraint determined based on the insurer’s ambiguous beliefs is not equivalent to a problem of optimal insurance design with a minimum expected retention determined based on the insurer’s ambiguous beliefs. Recently, Amarante, Ghossoub, and Phelps (2014) examined the problem of optimal insurance design with a premium constraint when the insurer has ambiguous beliefs. In particular, they showed that when the insurer is ambiguity-seeking, with a concave distortion of the insured’s probability measure, then the optimal indemnity schedule is a state-contingent deductible schedule, in which the deductible depends on the state of the world only through the insurer’s distortion function. In this paper, we examine the problem of optimal insurance design with a minimum expected retention constraint, in the case where the insurer is ambiguity-seeking. We obtain the aforementioned result of Amarante, Ghossoub, and Phelps (2014) and the classical result of Arrow (1971) as special cases.

Keywords: Optimal Insurance, Deductible, Minimum Retention, Ambiguity, Choquet Integral, Probability Distortion

JEL Classification: G22

Suggested Citation

Amarante, Massimiliano and Ghossoub, Mario, Optimal Insurance for a Minimal Expected Retention: The Case of an Ambiguity-Seeking Insurer (January 27, 2015). Risks, 4(1):8, 2016. Available at SSRN: https://ssrn.com/abstract=2556153 or http://dx.doi.org/10.2139/ssrn.2556153

Massimiliano Amarante

University of Montreal ( email )

C.P. 6128 succursale Centre-ville
Montreal, Quebec H3C 3J7
Canada

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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