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Rectangular Sets of Probability Measures

Alexander Shapiro

School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332

Operations Research 2016

In this paper we consider the notion of rectangularity of a set of probability measures from a somewhat different point of view. We define rectangularity as a property of dynamic decomposition of a distributionally robust stochastic optimization problem and show how it relates to the modern theory of coherent risk measures. Consequently, we discuss robust formulations of multistage stochastic optimization problems in frameworks of stochastic programming, stochastic optimal control, and Markov decision processes.

DOI
10.1287/opre.2015.1466
Volume
64 (2)
Pages
528-541
Language
en
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