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

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Author Info

  • Laetitia Andrieu

    (EDF R&D - EDF R&D Dept. OSIRIS - EDF)

  • Michel De Lara

    ()
    (CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - Ecole des Ponts ParisTech)

  • Babacar Seck

    (CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - Ecole des Ponts ParisTech)

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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.

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    Bibliographic Info

    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

    Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00390836/en/
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    Related research

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

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    1. Ogryczak, Wlodzimierz & Ruszczynski, Andrzej, 1999. "From stochastic dominance to mean-risk models: Semideviations as risk measures," European Journal of Operational Research, Elsevier, vol. 116(1), pages 33-50, July.
    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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