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

•Mean, covariance, average marginal third and fourth moments are matched exactly.•Scenarios and corresponding probability weights are produced without optimisation.•The algorithm is used in a mean-CVaR portfolio optimisation model.•Results show desirable in-sample and out-of-sample stability.•Good s...

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Bibliographic Details
Published in:European journal of operational research 2015-02, Vol.240 (3), p.678-687
Main Authors: Ponomareva, K., Roman, D., Date, P.
Format: Article
Language:English
Subjects:
Algorithms
Finance
Mathematical models
Mathematical problems
Matrix
Operations research
Optimization algorithms
OR in banking
Portfolio investments
Probability distribution
Scenarios
Stochastic programming
Studies
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Summary:•Mean, covariance, average marginal third and fourth moments are matched exactly.•Scenarios and corresponding probability weights are produced without optimisation.•The algorithm is used in a mean-CVaR portfolio optimisation model.•Results show desirable in-sample and out-of-sample stability.•Good solutions can be obtained with a relatively small number of scenarios. 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).
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2014.07.049