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Risk management in portfolio applications of non-convex stochastic programming

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  • Pang, Li-Ping
  • Chen, Shuang
  • Wang, Jin-He

Abstract

In this paper, we investigate a method to hedge nonconvex stochastic programming with CVaR constraints and apply the sample average approximation (SAA) method based on bundle method to solve it. Under some moderate conditions, the SAA solution converges to its true counterpart with probability approaching one. This technique is suitable for using by investment companies, brokerage firms, mutual funds, and any business that evaluates risks. It can be combined with analytical or scenario-based methods to optimize portfolios in which case the calculations often come down to non-convex programming. Finally, we illustrate our method by considering several portfolios in the Chinese stocks market.

Suggested Citation

  • Pang, Li-Ping & Chen, Shuang & Wang, Jin-He, 2015. "Risk management in portfolio applications of non-convex stochastic programming," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 565-575.
    • Handle: RePEc:eee:apmaco:v:258:y:2015:i:c:p:565-575
    DOI: 10.1016/j.amc.2015.02.031
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    References listed on IDEAS

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    1. Tobias Adrian & Hyun Song Shin, 2014. "Procyclical Leverage and Value-at-Risk," The Review of Financial Studies, Society for Financial Studies, vol. 27(2), pages 373-403.
    2. Paul Embrechts & Sidney Resnick & Gennady Samorodnitsky, 1999. "Extreme Value Theory as a Risk Management Tool," North American Actuarial Journal, Taylor & Francis Journals, vol. 3(2), pages 30-41.
    3. Yang Yang & Liping Pang & Xuefei Ma & Jie Shen, 2014. "Constrained Nonconvex Nonsmooth Optimization via Proximal Bundle Method," Journal of Optimization Theory and Applications, Springer, vol. 163(3), pages 900-925, December.
    4. 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.
    5. Jeremy Berkowitz & Peter Christoffersen & Denis Pelletier, 2011. "Evaluating Value-at-Risk Models with Desk-Level Data," Management Science, INFORMS, vol. 57(12), pages 2213-2227, December.
    6. Pérignon, Christophe & Smith, Daniel R., 2010. "The level and quality of Value-at-Risk disclosure by commercial banks," Journal of Banking & Finance, Elsevier, vol. 34(2), pages 362-377, February.
    7. Huifu Xu, 2010. "Sample Average Approximation Methods For A Class Of Stochastic Variational Inequality Problems," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 27(01), pages 103-119.
    8. Huang, Dashan & Zhu, Shushang & Fabozzi, Frank J. & Fukushima, Masao, 2010. "Portfolio selection under distributional uncertainty: A relative robust CVaR approach," European Journal of Operational Research, Elsevier, vol. 203(1), pages 185-194, May.
    9. 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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    Cited by:

    1. Zhang Qingye & Gao Yan, 2017. "An Asset Allocation Model and Its Solving Method," Journal of Systems Science and Information, De Gruyter, vol. 5(2), pages 163-175, April.

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