IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v240y2015i3p678-687.html
   My bibliography  Save this article

An algorithm for moment-matching scenario generation with application to financial portfolio optimisation

Author

Listed:
  • Ponomareva, K.
  • Roman, D.
  • Date, P.

Abstract

We present an algorithm for moment-matching scenario generation. This method produces scenarios and corresponding probability weights that match exactly the given mean, the covariance matrix, the average of the marginal skewness and the average of the marginal kurtosis of each individual component of a random vector. Optimisation is not employed in the scenario generation process and thus the method is computationally more advantageous than previous approaches. The algorithm is used for generating scenarios in a mean-CVaR portfolio optimisation model. For the chosen optimisation example, it is shown that desirable properties for a scenario generator are satisfied, including in-sample and out-of-sample stability. It is also shown that optimal solutions vary only marginally with increasing number of scenarios in this example; thus, good solutions can apparently be obtained with a relatively small number of scenarios. The proposed method can be used either on its own as a computationally inexpensive scenario generator or as a starting point for non-convex optimisation based scenario generators which aim to match all the third and the fourth order marginal moments (rather than average marginal moments).

Suggested Citation

  • Ponomareva, K. & Roman, D. & Date, P., 2015. "An algorithm for moment-matching scenario generation with application to financial portfolio optimisation," European Journal of Operational Research, Elsevier, vol. 240(3), pages 678-687.
    • Handle: RePEc:eee:ejores:v:240:y:2015:i:3:p:678-687
    DOI: 10.1016/j.ejor.2014.07.049
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037722171400616X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2014.07.049?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. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    2. James E. Smith, 1993. "Moment Methods for Decision Analysis," Management Science, INFORMS, vol. 39(3), pages 340-358, March.
    3. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    4. Ronald Hochreiter & Georg Pflug, 2007. "Financial scenario generation for stochastic multi-stage decision processes as facility location problems," Annals of Operations Research, Springer, vol. 152(1), pages 257-272, July.
    5. Topaloglou, Nikolas & Vladimirou, Hercules & Zenios, Stavros A., 2002. "CVaR models with selective hedging for international asset allocation," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1535-1561, July.
    6. Kjetil Høyland & Stein W. Wallace, 2001. "Generating Scenario Trees for Multistage Decision Problems," Management Science, INFORMS, vol. 47(2), pages 295-307, February.
    7. Philip M. Lurie & Matthew S. Goldberg, 1998. "An Approximate Method for Sampling Correlated Random Variables from Partially-Specified Distributions," Management Science, INFORMS, vol. 44(2), pages 203-218, February.
    8. Gulpinar, Nalan & Rustem, Berc & Settergren, Reuben, 2004. "Simulation and optimization approaches to scenario tree generation," Journal of Economic Dynamics and Control, Elsevier, vol. 28(7), pages 1291-1315, April.
    9. Christina Erlwein & Gautam Mitra & Diana Roman, 2012. "HMM based scenario generation for an investment optimisation problem," Annals of Operations Research, Springer, vol. 193(1), pages 173-192, March.
    10. 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)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Backe, Stian & Ahang, Mohammadreza & Tomasgard, Asgeir, 2021. "Stable stochastic capacity expansion with variable renewables: Comparing moment matching and stratified scenario generation sampling," Applied Energy, Elsevier, vol. 302(C).
    2. Li, Jinghua & Zhou, Jiasheng & Chen, Bo, 2020. "Review of wind power scenario generation methods for optimal operation of renewable energy systems," Applied Energy, Elsevier, vol. 280(C).
    3. Lee, Jinkyu & Bae, Sanghyeon & Kim, Woo Chang & Lee, Yongjae, 2023. "Value function gradient learning for large-scale multistage stochastic programming problems," European Journal of Operational Research, Elsevier, vol. 308(1), pages 321-335.
    4. Weiguo Zhang & Xiaolei He, 2022. "A New Scenario Reduction Method Based on Higher-Order Moments," INFORMS Journal on Computing, INFORMS, vol. 34(4), pages 1903-1918, July.
    5. Contreras, Juan Pablo & Bosch, Paul & Herrera, Mauricio, 2018. "Comment on “An algorithm for moment-matching scenario generation with application to financial portfolio optimization”," European Journal of Operational Research, Elsevier, vol. 269(3), pages 1180-1184.
    6. Bekiros, Stelios & Hernandez, Jose Arreola & Hammoudeh, Shawkat & Nguyen, Duc Khuong, 2015. "Multivariate dependence risk and portfolio optimization: An application to mining stock portfolios," Resources Policy, Elsevier, vol. 46(P2), pages 1-11.
    7. Ramponi, Federico Alessandro & Campi, Marco C., 2018. "Expected shortfall: Heuristics and certificates," European Journal of Operational Research, Elsevier, vol. 267(3), pages 1003-1013.
    8. Caio Mário Mesquita & Cristiano Arbex Valle & Adriano César Machado Pereira, 2024. "Scenario Generation for Financial Data with a Machine Learning Approach Based on Realized Volatility and Copulas," Computational Economics, Springer;Society for Computational Economics, vol. 63(5), pages 1879-1919, May.

    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. Mitra, Sovan & Lim, Sungmook & Karathanasopoulos, Andreas, 2019. "Regression based scenario generation: Applications for performance management," Operations Research Perspectives, Elsevier, vol. 6(C).
    2. Sun, Qi & Dong, Yucheng & Xu, Weidong, 2013. "Effects of higher order moments on the newsvendor problem," International Journal of Production Economics, Elsevier, vol. 146(1), pages 167-177.
    3. Caio Mário Mesquita & Cristiano Arbex Valle & Adriano César Machado Pereira, 2024. "Scenario Generation for Financial Data with a Machine Learning Approach Based on Realized Volatility and Copulas," Computational Economics, Springer;Society for Computational Economics, vol. 63(5), pages 1879-1919, May.
    4. Staino, Alessandro & Russo, Emilio, 2015. "A moment-matching method to generate arbitrage-free scenarios," European Journal of Operational Research, Elsevier, vol. 246(2), pages 619-630.
    5. Davari-Ardakani, Hamed & Aminnayeri, Majid & Seifi, Abbas, 2014. "A study on modeling the dynamics of statistically dependent returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 405(C), pages 35-51.
    6. Jiang, Yifu & Olmo, Jose & Atwi, Majed, 2024. "Dynamic robust portfolio selection under market distress," The North American Journal of Economics and Finance, Elsevier, vol. 69(PB).
    7. Libo Yin & Liyan Han, 2013. "Options strategies for international portfolios with overall risk management via multi-stage stochastic programming," Annals of Operations Research, Springer, vol. 206(1), pages 557-576, July.
    8. Wu, Dexiang & Wu, Desheng Dash, 2020. "A decision support approach for two-stage multi-objective index tracking using improved lagrangian decomposition," Omega, Elsevier, vol. 91(C).
    9. D. Kuhn, 2009. "Convergent Bounds for Stochastic Programs with Expected Value Constraints," Journal of Optimization Theory and Applications, Springer, vol. 141(3), pages 597-618, June.
    10. Vladimir Rankovic & Mikica Drenovak & Branko Uroševic & Ranko Jelic, 2016. "Mean Univariate-GARCH VaR Portfolio Optimization: Actual Portfolio Approach," CESifo Working Paper Series 5731, CESifo.
    11. Chen, Yan & Wang, Xuancheng, 2015. "A hybrid stock trading system using genetic network programming and mean conditional value-at-risk," European Journal of Operational Research, Elsevier, vol. 240(3), pages 861-871.
    12. Claudeci Da Silva & Hugo Agudelo Murillo & Joaquim Miguel Couto, 2014. "Early Warning Systems: Análise De Ummodelo Probit De Contágio De Crise Dos Estados Unidos Para O Brasil(2000-2010)," Anais do XL Encontro Nacional de Economia [Proceedings of the 40th Brazilian Economics Meeting] 110, ANPEC - Associação Nacional dos Centros de Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics].
    13. Zhao, Daping & Bai, Lin & Fang, Yong & Wang, Shouyang, 2022. "Multi‐period portfolio selection with investor views based on scenario tree," Applied Mathematics and Computation, Elsevier, vol. 418(C).
    14. 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.
    15. Topaloglou, Nikolas & Vladimirou, Hercules & Zenios, Stavros A., 2008. "A dynamic stochastic programming model for international portfolio management," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1501-1524, March.
    16. Al Janabi, Mazin A.M., 2014. "Optimal and investable portfolios: An empirical analysis with scenario optimization algorithms under crisis market prospects," Economic Modelling, Elsevier, vol. 40(C), pages 369-381.
    17. 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.
    18. Al Janabi, Mazin A.M. & Arreola Hernandez, Jose & Berger, Theo & Nguyen, Duc Khuong, 2017. "Multivariate dependence and portfolio optimization algorithms under illiquid market scenarios," European Journal of Operational Research, Elsevier, vol. 259(3), pages 1121-1131.
    19. Choi, Jaehyung & Kim, Young Shin & Mitov, Ivan, 2015. "Reward-risk momentum strategies using classical tempered stable distribution," Journal of Banking & Finance, Elsevier, vol. 58(C), pages 194-213.
    20. Shushang Zhu & Masao Fukushima, 2009. "Worst-Case Conditional Value-at-Risk with Application to Robust Portfolio Management," Operations Research, INFORMS, vol. 57(5), pages 1155-1168, October.

    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:eee:ejores:v:240:y:2015:i:3:p:678-687. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.