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Risk measurement with the equivalent utility principles

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Denuit, Michel [UCL] Laeven, Roger Kaas, Rob Goovaerts, Marc Dhaene, Jan

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.

Document type Article de périodique (Journal article) – Article de recherche
Publication date 2006
Language Anglais
Journal information "Statistics and Decisions : an international mathematical journal for stochastic methods and models" - Vol. 24, no. 1, p. 1-25 (2006)
Peer reviewed yes
Publisher Oldenbourg Wissenschaftsverlag GmbH ((Germany) Munich)
issn 0721-2631
Publication status Publié
Affiliations Louvain School of Management - CESAM - Center for Studies in Asset Management
UCL - Autre
Keywords Risk aversion ; Equivalent utility ; Axiomatic characterization ; Theories for decision under uncertainty ; Risk measures
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Bibliographic reference Denuit, Michel ; Laeven, Roger ; Kaas, Rob ; Goovaerts, Marc ; Dhaene, Jan. Risk measurement with the equivalent utility principles. In: Statistics and Decisions : an international mathematical journal for stochastic methods and models, Vol. 24, no. 1, p. 1-25 (2006)
Permanent URL http://hdl.handle.net/2078/16987