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DISAPPOINTMENT AVERSION PREMIUM PRINCIPLE

Published online by Cambridge University Press:  08 July 2015

Ka Chun Cheung ,
Wing Fung Chong ,
Robert Elliott  and
Sheung Chi Phillip Yam
Ka Chun Cheung
Affiliation:
Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong E-Mail: [email protected]
Wing Fung Chong
Affiliation:
Department of Statistics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong E-Mail: [email protected]
Robert Elliott
Affiliation:
School of Mathematical Sciences, University of Adelaide, Adelaide, Australia Haskayne School of Business, University of Calgary, Calgary, AB, Canada Centre for Applied Finance, University of South Australia, Adelaide, Australia E-Mail: [email protected]
Sheung Chi Phillip Yam
Affiliation:
Department of Statistics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong E-Mail: [email protected]
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Abstract

In recent years, the determination of premium principle under various non-expected utility frameworks has become popular, such as the pioneer works by Tsanakas and Desli (2003) and Kaluszka and Krzeszowiec (2012). We here revisit the problem under another prevalent behavioral economic theory, namely the Disappointment Aversion (DA) Theory proposed by Gul (1991). In this article, we define and study the properties of the DA premium principle, which builds on the equivalent utility premium principle. We derive various properties of this premium principle, such as non-negative and no unjustified risk loading, translation invariance, monotonicity, convexity, positive (non-)homogeneity, independent (non-)additivity, comonotonic (non-)additivity and monotonicity with respect to the extent of disappointment. A generalized Arrow–Pratt approximation is also established. Explicit representations of the premium principle are obtained for linear and exponential utilities, and they reveal that the premium principle proposed echoes the capital reserve regulatory requirement in practice.

Keywords

Disappointment aversion theoryequivalent utility premium principlegeneralized Arrow–Pratt approximationexplicit representationscapital reserve regulatory requirement
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 45 , Issue 3 , September 2015 , pp. 679 - 702
Copyright
Copyright © Astin Bulletin 2015 

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