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Living on the edge: how risky is it to operate at the limit of the tolerated risk?

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  • José Rodríguez-Mancilla

Abstract

This paper studies some of the implicit risks associated with strategies followed by a risk averse investor who maximizes the expected value of his final wealth, subject to a risk tolerance constraint characterized in terms of a convex risk measure such as Conditional Value-at-Risk. Embedded probability measures are uncovered using duality theory; these are used to assess the probability of surpassing a standard Value-at-Risk threshold. Using one of these embedded probabilities, a closed-form measure of the financial cost of hedging the loss exposure associated to the optimal strategies is derived and shown to be, under certain assumptions, a coherent measure of risk. Copyright Springer Science+Business Media, LLC 2010

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  • José Rodríguez-Mancilla, 2010. "Living on the edge: how risky is it to operate at the limit of the tolerated risk?," Annals of Operations Research, Springer, vol. 177(1), pages 21-45, June.
    • Handle: RePEc:spr:annopr:v:177:y:2010:i:1:p:21-45:10.1007/s10479-009-0604-6
    DOI: 10.1007/s10479-009-0604-6
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    References listed on IDEAS

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    1. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    2. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
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