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

Laetitia Andrieu (1) , Michel de Lara (2) , Babacar Seck (2)

1 EDF R&D OSIRIS - Optimisation, Simulation, Risque et Statistiques pour les Marchés de l’Energie
2 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique

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.

Mots clés: Risk measures; Utility functions; Nonexpected utility theory; Maxmin; Conditional Value-at-Risk; Loss aversion

Domaines: Gestion des risques [q-fin.RM]

Laetitia Andrieu, Michel de Lara, Babacar Seck. Conditional Value-at-Risk Constraint and Loss Aversion Utility Functions. 2008. ⟨hal-00390836⟩