Conditional Value-at-Risk Constraint and Loss Aversion Utility Functions

Laetitia Andrieu, Michel de Lara () and Babacar Seck
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Laetitia Andrieu: EDF R&D OSIRIS - Optimisation, Simulation, Risque et Statistiques pour les Marchés de l’Energie - EDF R&D - EDF R&D - EDF - EDF
Michel de Lara: CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - ENPC - École nationale des ponts et chaussées
Babacar Seck: CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - ENPC - École nationale des ponts et chaussées

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Abstract: We provide an economic interpretation of the practice consisting in incorporating risk measures as constraints in a classic expected return maximization problem. For what we call the infimum of expectations class of risk measures, we show that if the decision maker (DM) maximizes the expectation of a random return under constraint that the risk measure is bounded above, he then behaves as a ``generalized expected utility maximizer'' in the following sense. The DM exhibits ambiguity with respect to a family of utility functions defined on a larger set of decisions than the original one; he adopts pessimism and performs first a minimization of expected utility over this family, then performs a maximization over a new decisions set. This economic behaviour is called ``Maxmin under risk'' and studied by Maccheroni (2002). This economic interpretation allows us to exhibit a loss aversion factor when the risk measure is the Conditional Value-at-Risk.

Keywords: Risk measures; Utility functions; Nonexpected utility theory; Maxmin; Conditional Value-at-Risk; Loss aversion (search for similar items in EconPapers)
Date: 2008-12-26
Note: View the original document on HAL open archive server: https://hal.science/hal-00390836v1
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