Risk Measurement with Equivalent Utility Principles

26 Pages Posted: 2 Feb 2006

See all articles by Michel Denuit

Michel Denuit

Catholic University of Louvain

Jan Dhaene

Katholieke Universiteit Leuven

Marc Goovaerts

Catholic University of Leuven (KUL) - Department of Economics

Rob Kaas

University of Amsterdam - Faculty of Economics & Econometrics (FEE)

Roger J. A. Laeven

University of Amsterdam - Department of Quantitative Economics (KE)

Date Written: March 16, 2006

Abstract

Risk measures have been studied for several decades in the actuarial literature, where they appeared under the guise of premium calculation principles. Risk measures and properties that risk measures should satisfy have recently received considerable attention in the financial mathematics literature. Mathematically, a risk measure is a mapping from a class of random variables to the real line. Economically, a risk measure should capture the preferences of the decision-maker.

This paper complements the study initiated in Denuit, Dhaene & Van Wouwe (1999) and considers several theories for decision under uncertainty: the classical expected utility paradigm, Yaari's dual approach, maximin expected utility theory, Choquet expected utility theory and Quiggin's rank-dependent utility theory. Building on the actuarial equivalent utility pricing principle, broad classes of risk measures are generated, of which most classical risk measures appear to be particular cases. This approach shows that most risk measures studied recently in the financial mathematics literature disregard the utility concept (i.e., correspond to linear utilities), restricting their applicability. Some alternatives proposed in the literature are discussed.

Keywords: Risk measures, Theories for decision under uncertainty, Axiomatic characterization, Equivalent utility, Risk aversion

JEL Classification: D81, G10, G20

Suggested Citation

Denuit, Michel and Dhaene, Jan and Goovaerts, Marc and Kaas, Rob and Laeven, Roger Jean Auguste, Risk Measurement with Equivalent Utility Principles (March 16, 2006). Available at SSRN: https://ssrn.com/abstract=880007 or http://dx.doi.org/10.2139/ssrn.880007

Michel Denuit (Contact Author)

Catholic University of Louvain ( email )

Place Montesquieu, 3
B-1348 Louvain-la-Neuve, 1348
Belgium

Jan Dhaene

Katholieke Universiteit Leuven ( email )

Naamsestraat 69
Leuven, 3000
Belgium

Marc Goovaerts

Catholic University of Leuven (KUL) - Department of Economics ( email )

Leuven, B-3000
Belgium
+32 0 16 32 7446 (Phone)
+32 0 16 32 3740 (Fax)

Rob Kaas

University of Amsterdam - Faculty of Economics & Econometrics (FEE) ( email )

Roetersstraat 11
Amsterdam, 1018 WB
Netherlands

Roger Jean Auguste Laeven

University of Amsterdam - Department of Quantitative Economics (KE) ( email )

Valckenierstraat 65-67
Amsterdam, 1018 XE
Netherlands
+31 20 525 4252 (Phone)

HOME PAGE: http://www.rogerlaeven.com

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