Risk Measures and Theories of Choice
The final version of this article appeared as: Tsanakas A., E. Desli (2003), ''Risk measures and theories of choice'', British Actuarial Journal, 9(4), p.959-991.
40 Pages Posted: 13 Aug 2007 Last revised: 3 Jan 2014
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 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 Follmer and Shied (2002 a, b), and its properties lie between those of the exponential and distortion principles, which can be obtained as special cases.
Keywords: Risk Measures, Premium Calculation Principles, Coherent Measures of Risk, Distortion Premium Principle, Exponential Premium Principle, Expected Utility, Dual Theory of Choice Under Risk, Generalised Expected Utility
Suggested Citation: Suggested Citation
Do you have negative results from your research you’d like to share?
Recommended Papers
-
The Concept of Comonotonicity in Actuarial Science and Finance: Applications
By Jan Dhaene, Michel Denuit, ...
-
The Concept of Comonotonicity in Actuarial Science and Finance: Theory
By Jan Dhaene, Michel Denuit, ...
-
Comonotonicity and Maximal Stop-Loss Premiums
By Jan Dhaene, Shaun Wang, ...
-
Economic Capital Allocation Derived from Risk Measures
By Jan Dhaene, Marc Goovaerts, ...
-
Risk Measures and Comonotonicity: A Review
By Jan Dhaene, Steven Vanduffel, ...
-
Upper and Lower Bounds for Sums of Random Variables.
By Rob Kaas, Jan Dhaene, ...
-
Convex Upper and Lower Bounds for Present Value Functions
By David Vyncke, Marc Goovaerts, ...
-
Stochastic Upper Bounds for Present Value Functions
By Marc Goovaerts, Jan Dhaene, ...
-
A Simple Geometric Proof that Comonotonic Risks Have the Convex-Largest Sum
By Rob Kaas, Jan Dhaene, ...
-
Some New Classes of Consistent Risk Measures
By Marc Goovaerts, Rob Kaas, ...