Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/167875
Authors: 
Amarante, Massimiliano
Ghossoub, Mario
Year of Publication: 
2016
Citation: 
[Journal:] Risks [ISSN:] 2227-9091 [Volume:] 4 [Year:] 2016 [Issue:] 1 [Pages:] 1-27
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.
Subjects: 
optimal insurance
deductible
minimum retention
ambiguity
Choquet integral
probability distortion
JEL: 
G22
Persistent Identifier of the first edition: 
Creative Commons License: 
http://creativecommons.org/licenses/by/4.0/
Document Type: 
Article
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