A Heuristic for Moment-Matching Scenario Generation
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In stochastic programming models we always face the problem of how to represent the random variables. This is particularly difficult with multidimensional distributions. We present an algorithm that produces a discrete joint distribution consistent with specified values of the first four marginal moments and correlations. The joint distribution is constructed by decomposing the multivariate problem into univariate ones, and using an iterative procedure that combines simulation, Cholesky decomposition and various transformations to achieve the correct correlations without changing the marginal moments.
With the algorithm, we can generate 1000 one-period scenarios for 12 random variables in 16 seconds, and for 20 random variables in 48 seconds, on a Pentium III machine.
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- 1.D.R. Cariño and W.T. Ziemba, “Formulation of the Russell-Yasuda Kasai financial planning model,” Operations Research, vol. 46, no. 4, pp. 443-449, 1998.Google Scholar
- 2.G. Consigli and M.A.H. Dempster, “Dynamic stochastic programming for asset-liability management,” Annals of Operations Research, vol. 81, pp. 131-162, 1998.Google Scholar
- 3.C. Dert, “Asset liability management for pension funds, a multistage chance constrained programming approach,” PhD Thesis, Erasmus University, Rotterdam, The Netherlands, 1995.Google Scholar
- 4.A.I. Fleishman, “A method for simulating nonnormal distributions,” Psychometrika, vol. 43, pp. 521-532, 1978.Google Scholar
- 5.N.J. Higham, “Computing the nearest correlation matrix—Aproblem from finance,” Numerical Analysis Report No. 369, Manchester Centre for Computational Mathematics, Manchester, England, 2000.Google Scholar
- 6.K. HØyland and S.W. Wallace, “Generating scenario trees for multistage decision problems,” Management Science, vol. 47, no. 2, pp. 295-307, 2001.Google Scholar
- 7.P.M. Lurie and M.S. Goldberg, “An approximate method for sampling correlated random variables from partially-specified distributions,” Management Science, vol. 44, no. 2, pp. 203-218, 1998.Google Scholar
- 8.J.M. Mulvey, “Generating scenarios for the Towers Perrin investment system,” Interfaces, vol. 26, pp. 1-13, 1996.Google Scholar
- 9.C.D. Vale and V.A. Maurelli, “Simulating multivariate nonnormal distributions,” Psychometrika, vol. 48, no. 3, pp. 465-471, 1983.Google Scholar