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

  • Laetitia Andrieu

    (EDF R&D - EDF R&D Dept. OSIRIS - EDF - Electricité de France)

  • Michel De Lara


    (CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - École des Ponts ParisTech (ENPC) - UPE - Université Paris-Est)

  • Babacar Seck

    (CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - École des Ponts ParisTech (ENPC) - UPE - Université Paris-Est)

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    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.

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    Paper provided by HAL in its series Working Papers with number hal-00390836.

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    Date of creation: 26 Dec 2008
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    Handle: RePEc:hal:wpaper:hal-00390836
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    1. W. Ogryczak & A. Ruszczynski, 1997. "From Stochastic Dominance to Mean-Risk Models: Semideviations as Risk Measures," Working Papers ir97027, International Institute for Applied Systems Analysis.
    2. Dentcheva, Darinka & Ruszczynski, Andrzej, 2006. "Portfolio optimization with stochastic dominance constraints," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 433-451, February.
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