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Consistency of sample estimates of risk averse stochastic programs

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

Abstract: In this paper we study asymptotic consistency of law invariant convex risk measures and the corresponding risk averse stochastic programming problems for independent identically distributed data. Under mild regularity conditions we prove a Law of Large Numbers and epiconvergence of the corresponding statistical estimators. This can be applied in a straight forward way to establishing convergence w.p.1 of sample based estimators of risk averse stochastic programming problems.

Keywords: Law invariant convex and coherent risk measures, stochastic programming, Law of Large Numbers, consistency of statistical estimators, epiconvergence, sample average approximation

Category 1: Stochastic Programming

Citation: Preprint

Download: [PDF]

Entry Submitted: 04/20/2012
Entry Accepted: 04/20/2012
Entry Last Modified: 09/29/2012

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