Geodesic
Numerical study of discretizations of multistage stochastic programs
Kybernetika, Tome 44 (2008) no. 2, pp. 185-204.

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This paper presents a numerical study of a deterministic discretization procedure for multistage stochastic programs where the underlying stochastic process has a continuous probability distribution. The discretization procedure is based on quasi-Monte Carlo techniques originally developed for numerical multivariate integration. The solutions of the discretized problems are evaluated by statistical bounds obtained from random sample average approximations and out-of-sample simulations. In the numerical tests, the optimal values of the discretizations as well as their first-stage solutions approach those of the original infinite-dimensional problem as the discretizations are made finer.
Classification : 49M25, 90C15, 90C25
Keywords: stochastic programming; discretization; integration quadratures; simulation 
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     author = {Hilli, Petri and Pennanen, Teemu},
     title = {Numerical study of discretizations of multistage stochastic programs},
     journal = {Kybernetika},
     pages = {185--204},
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     volume = {44},
     number = {2},
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     zbl = {1154.90556},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2008__44_2_a4/}
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Hilli, Petri; Pennanen, Teemu. Numerical study of discretizations of multistage stochastic programs. Kybernetika, Tome 44 (2008) no. 2, pp. 185-204. http://geodesic.mathdoc.fr/item/KYB_2008__44_2_a4/