Tree approximation for discrete time stochastic processes: a process distance approach

Raimund Kovacevic () and Alois Pichler

Annals of Operations Research, 2015, vol. 235, issue 1, 395-421

Abstract: 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. Copyright Springer Science+Business Media New York 2015

Keywords: Stochastic processes and trees; Wasserstein and Kantorovich distance; Tree approximation; Optimal transport; Facility location; 90C15; 60B05; 90-08 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (11)

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DOI: 10.1007/s10479-015-1994-2

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