IDEAS home Printed from https://ideas.repec.org/a/spr/comgts/v12y2015i2p221-242.html
   My bibliography  Save this article

On variance reduction of mean-CVaR Monte Carlo estimators

Author

Listed:
  • Václav Kozmík

Abstract

We formulate an objective as a convex combination of expectation and risk, measured by the $$\mathrm{CVaR }$$ CVaR risk measure. The poor performance of standard Monte Carlo estimators applied on functions of this form is discussed and a variance reduction scheme based on importance sampling is proposed. We provide analytical solution for random variables based on normal distribution and outline the way for the other distributions, either by analytical computation or by sampling. Our results are applied in the framework of stochastic dual dynamic programming algorithm. Computational results which validate the previous analysis are given. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Václav Kozmík, 2015. "On variance reduction of mean-CVaR Monte Carlo estimators," Computational Management Science, Springer, vol. 12(2), pages 221-242, April.
    • Handle: RePEc:spr:comgts:v:12:y:2015:i:2:p:221-242
    DOI: 10.1007/s10287-014-0225-7
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10287-014-0225-7
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10287-014-0225-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Denneberg, Dieter, 1990. "Premium Calculation: Why Standard Deviation Should be Replaced by Absolute Deviation1," ASTIN Bulletin, Cambridge University Press, vol. 20(2), pages 181-190, November.
    2. Shapiro, Alexander, 2011. "Analysis of stochastic dual dynamic programming method," European Journal of Operational Research, Elsevier, vol. 209(1), pages 63-72, February.
    3. Rudloff, Birgit & Street, Alexandre & Valladão, Davi M., 2014. "Time consistency and risk averse dynamic decision models: Definition, interpretation and practical consequences," European Journal of Operational Research, Elsevier, vol. 234(3), pages 743-750.
    4. Andy Philpott & Vitor de Matos & Erlon Finardi, 2013. "On Solving Multistage Stochastic Programs with Coherent Risk Measures," Operations Research, INFORMS, vol. 61(4), pages 957-970, August.
    5. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    6. Güzin Bayraksan & David P. Morton, 2011. "A Sequential Sampling Procedure for Stochastic Programming," Operations Research, INFORMS, vol. 59(4), pages 898-913, August.
    7. 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.
    8. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Davi Valladão & Thuener Silva & Marcus Poggi, 2019. "Time-consistent risk-constrained dynamic portfolio optimization with transactional costs and time-dependent returns," Annals of Operations Research, Springer, vol. 282(1), pages 379-405, November.
    2. Mahmutoğulları, Ali İrfan & Çavuş, Özlem & Aktürk, M. Selim, 2018. "Bounds on risk-averse mixed-integer multi-stage stochastic programming problems with mean-CVaR," European Journal of Operational Research, Elsevier, vol. 266(2), pages 595-608.
    3. Strub, Moris S. & Li, Duan & Cui, Xiangyu & Gao, Jianjun, 2019. "Discrete-time mean-CVaR portfolio selection and time-consistency induced term structure of the CVaR," Journal of Economic Dynamics and Control, Elsevier, vol. 108(C).
    4. Powell, Warren B., 2019. "A unified framework for stochastic optimization," European Journal of Operational Research, Elsevier, vol. 275(3), pages 795-821.
    5. Weini Zhang & Hamed Rahimian & Güzin Bayraksan, 2016. "Decomposition Algorithms for Risk-Averse Multistage Stochastic Programs with Application to Water Allocation under Uncertainty," INFORMS Journal on Computing, INFORMS, vol. 28(3), pages 385-404, August.
    6. Rudloff, Birgit & Street, Alexandre & Valladão, Davi M., 2014. "Time consistency and risk averse dynamic decision models: Definition, interpretation and practical consequences," European Journal of Operational Research, Elsevier, vol. 234(3), pages 743-750.
    7. Schur, Rouven & Gönsch, Jochen & Hassler, Michael, 2019. "Time-consistent, risk-averse dynamic pricing," European Journal of Operational Research, Elsevier, vol. 277(2), pages 587-603.
    8. Martin Šmíd & Václav Kozmík, 2024. "Approximation of multistage stochastic programming problems by smoothed quantization," Review of Managerial Science, Springer, vol. 18(7), pages 2079-2114, July.
    9. Daniel R. Jiang & Warren B. Powell, 2018. "Risk-Averse Approximate Dynamic Programming with Quantile-Based Risk Measures," Mathematics of Operations Research, INFORMS, vol. 43(2), pages 554-579, May.
    10. Adam, Alexandre & Houkari, Mohamed & Laurent, Jean-Paul, 2008. "Spectral risk measures and portfolio selection," Journal of Banking & Finance, Elsevier, vol. 32(9), pages 1870-1882, September.
    11. Cui, Xueting & Zhu, Shushang & Sun, Xiaoling & Li, Duan, 2013. "Nonlinear portfolio selection using approximate parametric Value-at-Risk," Journal of Banking & Finance, Elsevier, vol. 37(6), pages 2124-2139.
    12. Vladimir Rankovic & Mikica Drenovak & Branko Uroševic & Ranko Jelic, 2016. "Mean Univariate-GARCH VaR Portfolio Optimization: Actual Portfolio Approach," CESifo Working Paper Series 5731, CESifo.
    13. Harris, Richard D.F. & Mazibas, Murat, 2013. "Dynamic hedge fund portfolio construction: A semi-parametric approach," Journal of Banking & Finance, Elsevier, vol. 37(1), pages 139-149.
    14. Rad, Hossein & Low, Rand Kwong Yew & Miffre, Joëlle & Faff, Robert, 2020. "Does sophistication of the weighting scheme enhance the performance of long-short commodity portfolios?," Journal of Empirical Finance, Elsevier, vol. 58(C), pages 164-180.
    15. Moret, Fabio & Pinson, Pierre & Papakonstantinou, Athanasios, 2020. "Heterogeneous risk preferences in community-based electricity markets," European Journal of Operational Research, Elsevier, vol. 287(1), pages 36-48.
    16. Karma, Otto & Sander, Priit, 2006. "The impact of financial leverage on risk of equity measured by loss-oriented risk measures: An option pricing approach," European Journal of Operational Research, Elsevier, vol. 175(3), pages 1340-1356, December.
    17. Yuichi Takano & Renata Sotirov, 2012. "A polynomial optimization approach to constant rebalanced portfolio selection," Computational Optimization and Applications, Springer, vol. 52(3), pages 645-666, July.
    18. A. B. Philpott & V. L. Matos & L. Kapelevich, 2018. "Distributionally robust SDDP," Computational Management Science, Springer, vol. 15(3), pages 431-454, October.
    19. Hsieh, Chung-Chi & Lu, Yu-Ting, 2010. "Manufacturer's return policy in a two-stage supply chain with two risk-averse retailers and random demand," European Journal of Operational Research, Elsevier, vol. 207(1), pages 514-523, November.
    20. Dan A. Iancu & Marek Petrik & Dharmashankar Subramanian, 2015. "Tight Approximations of Dynamic Risk Measures," Mathematics of Operations Research, INFORMS, vol. 40(3), pages 655-682, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:comgts:v:12:y:2015:i:2:p:221-242. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.