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SPEPS Preprint

Author(s): Matti Koivu, Helsinki School of Economics
Title: Variance reduction in sample approximations of stochastic programs
Date of Acceptance: 02.10.2004
Submission Date: 23.04.2004
Series Title: Stochastic Programming E-Print Series
(SPEPS)
Editors: Julie L. Higle; Werner Römisch; Surrajeet Sen
Keywords (eng): Stochastic optimization, discretization, varinace reduction techniques, randomizes quasi-monte carlo methods, antithetic variates
Appeared in: Mathematical programming 3 (Vol. 103, 2005)
Springer (Berlin [u.a.])
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Abstract (eng):
This paper studies the use of randomized Quasi-Monte Carlo methods (RQMC) in sample approximations of stochastic programs. In high dimensional numerical integration, RQMC methods often substantially reduce the variance of sample approximations compared to MC. It seems thus natural to use RQMC methods in sample approximations of stochastic programs. It is shown, that RQMC methods produce epi-convergent approximations of the original problem. RQMC and MC methods are compared numerically in five different portfolio management models. In the tests, RQMC methods outperform MC sampling substantially reducing the sample variance and bias of optimal values in all the considered problems.
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