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Computational aspects of minimizing conditional value-at-risk

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  • Alexandra Künzi-Bay

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  • János Mayer
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    Abstract

    We consider optimization problems for minimizing conditional value-at-risk (CVaR) from a computational point of view, with an emphasis on financial applications. As a general solution approach, we suggest to reformulate these CVaR optimization problems as two-stage recourse problems of stochastic programming. Specializing the L-shaped method leads to a new algorithm for minimizing conditional value-at-risk. We implemented the algorithm as the solver CVaRMin. For illustrating the performance of this algorithm, we present some comparative computational results with two kinds of test problems. Firstly, we consider portfolio optimization problems with 5 random variables. Such problems involving conditional value at risk play an important role in financial risk management. Therefore, besides testing the performance of the proposed algorithm, we also present computational results of interest in finance. Secondly, with the explicit aim of testing algorithm performance, we also present comparative computational results with randomly generated test problems involving 50 random variables. In all our tests, the experimental solver, based on the new approach, outperformed by at least one order of magnitude all general-purpose solvers, with an accuracy of solution being in the same range as that with the LP solvers. Copyright Springer-Verlag Berlin/Heidelberg 2006

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    File URL: http://hdl.handle.net/10.1007/s10287-005-0042-0
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    Bibliographic Info

    Article provided by Springer in its journal Computational Management Science.

    Volume (Year): 3 (2006)
    Issue (Month): 1 (01)
    Pages: 3-27

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    Handle: RePEc:spr:comgts:v:3:y:2006:i:1:p:3-27

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    Web page: http://www.springerlink.com/link.asp?id=111894

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    Related research

    Keywords: Conditional value-at-risk; Stochastic programming; Mathematical programming algorithms; Stochastic models; Finance; Portfolio optimization; Risk management;

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    Cited by:
    1. Csaba Fábián & Olga Papp & Krisztián Eretnek, 2013. "Implementing the simplex method as a cutting-plane method, with a view to regularization," Computational Optimization and Applications, Springer, vol. 56(2), pages 343-368, October.
    2. Pu Huang & Dharmashankar Subramanian, 2012. "Iterative estimation maximization for stochastic linear programs with conditional value-at-risk constraints," Computational Management Science, Springer, vol. 9(4), pages 441-458, November.
    3. Roman, Diana & Mitra, Gautam & Zverovich, Victor, 2013. "Enhanced indexation based on second-order stochastic dominance," European Journal of Operational Research, Elsevier, vol. 228(1), pages 273-281.
    4. Włodzimierz Ogryczak & Tomasz Śliwiński, 2011. "On solving the dual for portfolio selection by optimizing Conditional Value at Risk," Computational Optimization and Applications, Springer, vol. 50(3), pages 591-595, December.
    5. Fábián, Csaba I., 2008. "Handling CVaR objectives and constraints in two-stage stochastic models," European Journal of Operational Research, Elsevier, vol. 191(3), pages 888-911, December.
    6. Mansini, Renata & Ogryczak, Wlodzimierz & Speranza, M. Grazia, 2014. "Twenty years of linear programming based portfolio optimization," European Journal of Operational Research, Elsevier, vol. 234(2), pages 518-535.
    7. Fanwen Meng & Jie Sun & Mark Goh, 2011. "A smoothing sample average approximation method for stochastic optimization problems with CVaR risk measure," Computational Optimization and Applications, Springer, vol. 50(2), pages 379-401, October.

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