期刊
ANNALS OF OPERATIONS RESEARCH
卷 235, 期 1, 页码 395-421出版社
SPRINGER
DOI: 10.1007/s10479-015-1994-2
关键词
Stochastic processes and trees; Wasserstein and Kantorovich distance; Tree approximation; Optimal transport; Facility location
资金
- Austrian science fund FWF [P 24125-N13]
- Research Council of Norway [207690/E20]
- Austrian Science Fund (FWF) [P 24125] Funding Source: researchfish
Approximating stochastic processes by scenario trees is important in decision analysis. In this paper we focus on improving the approximation quality of trees by smaller, tractable trees. In particular we propose and analyze an iterative algorithm to construct improved approximations: given a stochastic process in discrete time and starting with an arbitrary, approximating tree, the algorithm improves both, the probabilities on the tree and the related path-values of the smaller tree, leading to significantly improved approximations of the initial stochastic process. The quality of the approximation is measured by the process distance (nested distance), which was introduced recently. For the important case of quadratic process distances the algorithm finds locally best approximating trees in finitely many iterations by generalizing multistage k-means clustering.
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