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June 2013 Consistency of sample estimates of risk averse stochastic programs
Alexander Shapiro
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J. Appl. Probab. 50(2): 533-541 (June 2013). DOI: 10.1239/jap/1371648959

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 straightforward way to establish convergence with probability 1 of sample-based estimators of risk averse stochastic programming problems.

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Alexander Shapiro. "Consistency of sample estimates of risk averse stochastic programs." J. Appl. Probab. 50 (2) 533 - 541, June 2013. https://doi.org/10.1239/jap/1371648959

Information

Published: June 2013
First available in Project Euclid: 19 June 2013

zbMATH: 1301.62045
MathSciNet: MR3102498
Digital Object Identifier: 10.1239/jap/1371648959

Subjects:
Primary: 62F12
Secondary: 90C15

Rights: Copyright © 2013 Applied Probability Trust

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Vol.50 • No. 2 • June 2013
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