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

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  • 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
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    References listed on IDEAS

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    Cited by:

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    2. 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.
    3. 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.
    4. 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).
    5. 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.
    6. 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.
    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.

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