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Consistency of Sample Estimates of Risk Averse Stochastic Programs

Part of: Parametric inference

Published online by Cambridge University Press:  30 January 2018

Alexander Shapiro
Alexander Shapiro*
Affiliation:
Georgia Institute of Technology
*
∗ Postal address: Georgia Institute of Technology, School of Industrial and Systems Engineering, 765 Ferst Drive, Atlanta, GA 30332, USA. Email address: ashapiro@isye.gatech.edu
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Abstract

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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.

Keywords

Law invariant convex and coherent risk measuresstochastic programminglaw of large numbersconsistency of statistical estimatorsepiconvergencesample average approximation

MSC classification

Primary: 62F12: Asymptotic properties of estimators
Secondary: 90C15: Stochastic programming
Type
Research Article
Information
Journal of Applied Probability , Volume 50 , Issue 2 , June 2013 , pp. 533 - 541
Copyright
© Applied Probability Trust 

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