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Type: Journal article
Title: Disappointment aversion premium principle
Author: Cheung, K.
Chong, W.
Elliott, R.
Yam, S.
Citation: Astin Bulletin: The Journal of the ASTIN and AFIR Sections of the International Actuarial Association, 2015; 45(3):679-702
Publisher: Cambridge University Press
Issue Date: 2015
ISSN: 0515-0361
Statement of
Ka Chun Cheun, Wing Fung Chong, Robert Elliott, and Sheung Chi Phillip Yam
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 theory; equivalent utility premium principle; general- ized Arrow–Pratt approximation; explicit representations; capital reserve regu- latory requirement
Rights: © by Astin Bulletin 2015
DOI: 10.1017/asb.2015.12
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