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An algorithm for sequential tail value at risk for path-independent payoffs in a binomial tree

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  • Berend Roorda

Abstract

We present an algorithm that determines Sequential Tail Value at Risk (STVaR) for path-independent payoffs in a binomial tree. STVaR is a dynamic version of Tail-Value-at-Risk (TVaR) characterized by the property that risk levels at any moment must be in the range of risk levels later on. The algorithm consists of a finite sequence of backward recursions that is guaranteed to arrive at the solution of the corresponding dynamic optimization problem. The algorithm makes concrete how STVaR differs from TVaR over the remaining horizon, and from recursive TVaR, which amounts to Dynamic Programming. Algorithmic aspects are compared with the cutting-plane method. Time consistency and comonotonicity properties are illustrated by applying the algorithm on elementary examples. Copyright The Author(s) 2010

Suggested Citation

  • Berend Roorda, 2010. "An algorithm for sequential tail value at risk for path-independent payoffs in a binomial tree," Annals of Operations Research, Springer, vol. 181(1), pages 463-483, December.
    • Handle: RePEc:spr:annopr:v:181:y:2010:i:1:p:463-483:10.1007/s10479-010-0761-7
    DOI: 10.1007/s10479-010-0761-7
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    References listed on IDEAS

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    1. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath & Hyejin Ku, 2007. "Coherent multiperiod risk adjusted values and Bellman’s principle," Annals of Operations Research, Springer, vol. 152(1), pages 5-22, July.
    2. Alexandra Künzi-Bay & János Mayer, 2006. "Computational aspects of minimizing conditional value-at-risk," Computational Management Science, Springer, vol. 3(1), pages 3-27, January.
    3. Roorda, Berend & Schumacher, J.M., 2007. "Time consistency conditions for acceptability measures, with an application to Tail Value at Risk," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 209-230, March.
    4. Tapiero, Charles, 2003. "Value at Risk and Inventory Control," ESSEC Working Papers DR 03012, ESSEC Research Center, ESSEC Business School.
    5. 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.
    6. 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.
    7. Willem Haneveld & Maarten Vlerk, 2006. "Integrated Chance Constraints: Reduced Forms and an Algorithm," Computational Management Science, Springer, vol. 3(4), pages 245-269, September.
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    Cited by:

    1. Fasen Vicky & Svejda Adela, 2012. "Time consistency of multi-period distortion measures," Statistics & Risk Modeling, De Gruyter, vol. 29(2), pages 133-153, June.

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