Optimal Insurance for a Minimal Expected Retention: The Case of an Ambiguity-Seeking Insurer
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,...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2016-03-01
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| Series: | Risks |
| Subjects: | |
| Online Access: | http://www.mdpi.com/2227-9091/4/1/8 |
| _version_ | 1818530096735059968 |
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| author | Massimiliano Amarante Mario Ghossoub |
| author_facet | Massimiliano Amarante Mario Ghossoub |
| author_sort | Massimiliano Amarante |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-11T17:15:25Z |
| format | Article |
| id | doaj.art-773436334f094a139f9984597a56794b |
| institution | Directory Open Access Journal |
| issn | 2227-9091 |
| language | English |
| last_indexed | 2024-12-11T17:15:25Z |
| publishDate | 2016-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Risks |
| spelling | doaj.art-773436334f094a139f9984597a56794b2022-12-22T00:57:22ZengMDPI AGRisks2227-90912016-03-0141810.3390/risks4010008risks4010008Optimal Insurance for a Minimal Expected Retention: The Case of an Ambiguity-Seeking InsurerMassimiliano Amarante0Mario Ghossoub1Département de Sciences Économiques, Université de Montréal, C.P. 6128, succursale Centre-ville, Montréal, QC H3C 3J7, CanadaImperial College London, South Kensington Campus, London SW7 2AZ, UKIn 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.http://www.mdpi.com/2227-9091/4/1/8optimal insurancedeductibleminimum retentionambiguityChoquet integralprobability distortion |
| spellingShingle | Massimiliano Amarante Mario Ghossoub Optimal Insurance for a Minimal Expected Retention: The Case of an Ambiguity-Seeking Insurer Risks optimal insurance deductible minimum retention ambiguity Choquet integral probability distortion |
| title | Optimal Insurance for a Minimal Expected Retention: The Case of an Ambiguity-Seeking Insurer |
| title_full | Optimal Insurance for a Minimal Expected Retention: The Case of an Ambiguity-Seeking Insurer |
| title_fullStr | Optimal Insurance for a Minimal Expected Retention: The Case of an Ambiguity-Seeking Insurer |
| title_full_unstemmed | Optimal Insurance for a Minimal Expected Retention: The Case of an Ambiguity-Seeking Insurer |
| title_short | Optimal Insurance for a Minimal Expected Retention: The Case of an Ambiguity-Seeking Insurer |
| title_sort | optimal insurance for a minimal expected retention the case of an ambiguity seeking insurer |
| topic | optimal insurance deductible minimum retention ambiguity Choquet integral probability distortion |
| url | http://www.mdpi.com/2227-9091/4/1/8 |
| work_keys_str_mv | AT massimilianoamarante optimalinsuranceforaminimalexpectedretentionthecaseofanambiguityseekinginsurer AT marioghossoub optimalinsuranceforaminimalexpectedretentionthecaseofanambiguityseekinginsurer |