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Rectangular sets of probability measures

Alexander Shapiro (ashapiro***at***isye.gatech.edu)

Abstract: In this paper we consider the notion of rectangularity of a set of probability measures, introduced in Epstein and Schneider (2003), 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.

Keywords: Multistage stochastic optimization, rectangularity, risk averse optimization, robust optimal control and Markov decision processes, dynamic programming, coherent risk measures, time consistency.

Category 1: Stochastic Programming


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Entry Submitted: 10/24/2014
Entry Accepted: 10/24/2014
Entry Last Modified: 10/13/2015

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