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Risks 2016, 4(1), 8; doi:10.3390/risks4010008

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

1
Département de Sciences Économiques, Université de Montréal, C.P. 6128, succursale Centre-ville, Montréal, QC H3C 3J7, Canada
2
Imperial College London, South Kensington Campus, London SW7 2AZ, UK
*
Author to whom correspondence should be addressed.
Academic Editor: Alexander Szimayer
Received: 22 December 2015 / Revised: 7 March 2016 / Accepted: 9 March 2016 / Published: 21 March 2016
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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, this equivalence no longer holds. Recently, Amarante, Ghossoub and Phelps 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 and the classical result of Arrow as special cases. View Full-Text
Keywords: optimal insurance; deductible; minimum retention; ambiguity; Choquet integral; probability distortion optimal insurance; deductible; minimum retention; ambiguity; Choquet integral; probability distortion
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Amarante, M.; Ghossoub, M. Optimal Insurance for a Minimal Expected Retention: The Case of an Ambiguity-Seeking Insurer. Risks 2016, 4, 8.

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