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OPTIMAL INSURANCE CONTRACTS UNDER DISTORTION RISK MEASURES WITH AMBIGUITY AVERSION

Published online by Cambridge University Press:  11 May 2020

Wenjun Jiang ,
Marcos Escobar-Anel  and
Jiandong Ren
Wenjun Jiang*
Affiliation:
Department of Mathematics and Statistics, University of Calgary, Calgary, AlbertaT2N 1N4, Canada, E-mail: wenjun.jiang@ucalgary.ca
Marcos Escobar-Anel
Affiliation:
Department of Statistical and Actuarial Sciences, University of Western Ontario, London, OntarioN6A 3K7, Canada
Jiandong Ren
Affiliation:
Department of Statistical and Actuarial Sciences, University of Western Ontario, London, OntarioN6A 3K7, Canada
*
E-mail: wenjun.jiang@ucalgary.ca
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Abstract

This paper presents analytical representations for an optimal insurance contract under distortion risk measure and in the presence of model uncertainty. We incorporate ambiguity aversion and distortion risk measure through the model of Robert and Therond [(2014) ASTIN Bulletin: The Journal of the IAA, 44(2), 277–302.] as per the framework of Klibanoff et al. [(2005) A smooth model of decision making under ambiguity. Econometrica, 73(6), 1849–1892.]. Explicit optimal insurance indemnity functions are derived when the decision maker (DM) applies Value-at-Risk as risk measure and is ambiguous about the loss distribution. Our results show that: (1) under model uncertainty, ambiguity aversion results in a distorted probability distribution over the set of possible models with a bias in favor of the model which yields a larger risk; (2) a more ambiguity-averse DM would demand more insurance coverage; (3) for a given budget, uncertainties about the loss distribution result in higher risk level for the DM.

Keywords

Optimal insurancemodel uncertaintydistortion risk measureambiguity aversionKarush–Kuhn–Tucker multiplierscalculus of variationsuboptimal contract
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 50 , Issue 2 , May 2020 , pp. 619 - 646
Copyright
© Astin Bulletin 2020

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