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Analytical Bounds for two Value-at-Risk Functionals

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  • Hürlimann, Werner

Abstract

Based on the notions of value-at-risk and conditional value-at-risk, we consider two functionals, abbreviated VaR and CVaR, which represent the economic risk capital required to operate a risky business over some time period when only a small probability of loss is tolerated. These functionals are consistent with the risk preferences of profit-seeking (and risk averse) decision makers and preserve the stochastic dominance order (and the stop-loss order). This result is used to bound the VaR and CVaR functionals by determining their maximal values over the set of all loss and profit functions with fixed first few moments. The evaluation of CVaR for the aggregate loss of portfolios is also discussed. The results of VaR and CVaR calculations are illustrated and compared at some typical situations of general interest.

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  • Hürlimann, Werner, 2002. "Analytical Bounds for two Value-at-Risk Functionals," ASTIN Bulletin, Cambridge University Press, vol. 32(2), pages 235-265, November.
    • Handle: RePEc:cup:astinb:v:32:y:2002:i:02:p:235-265_01
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    Cited by:

    1. Grzegorz Darkiewicz & Griselda Deelstra & Jan Dhaene & Tom Hoedemakers & Michèle Vanmaele, 2009. "Bounds for Right Tails of Deterministic and Stochastic Sums of Random Variables," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(4), pages 847-866, December.

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