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Risk Measures and Theories of Choice

Published online by Cambridge University Press:  10 June 2011

A. Tsanakas  and
E. Desli
A. Tsanakas
Affiliation:
Market Risk and Reserving Unit, Lloyd's of London, One Lime Street, London EC3M 7HA, U.K., Tel: +44(0)20-7327-5268, Fax: +44(0)20-7327-5658, Email: andreas.tsanakas@lloyds.com.
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Abstract

We discuss classes of risk measures in terms both of their axiomatic definitions and of the economic theories of choice that they can be derived from. More specifically, expected utility theory gives rise to the exponential premium principle, proposed by Gerber (1974), Dhaene et al. (2003), whereas Yaari's (1987) dual theory of choice under risk can be viewed as the source of the distortion premium principle (Denneberg, 1990; Wang, 1996). We argue that the properties of the exponential and distortion premium principles are complementary, without either of the two performing completely satisfactorily as a risk measure. Using generalised expected utility theory (Quiggin, 1993), we derive a new risk measure, which we call the distortion-exponential principle. This risk measure satisfies the axioms of convex measures of risk, proposed by Föllmer & Shied (2002a,b), and its properties lie between those of the exponential and distortion principles, which can be obtained as special cases.

Keywords

Risk MeasuresPremium Calculation PrinciplesCoherent Measures of RiskDistortion Premium PrincipleExponential Premium PrincipleExpected UtilityDual Theory of Choice Under RiskGeneralised Expected Utility
Type
Sessional meetings: papers and abstracts of discussions
Information
British Actuarial Journal , Volume 9 , Issue 4 , 01 October 2003 , pp. 959 - 991
Copyright
Copyright © Institute and Faculty of Actuaries 2003

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