Consistency of sample estimates of risk averse stochastic programs

Published: 2012/04/20, Updated: 2012/09/29

Stochastic Programming consistency of statistical estimators, epiconvergence, law invariant convex and coherent risk measures, law of large numbers, sample average approximation, stochastic programming Short URL: https://optimization-online.org/?p=12005

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.

Consistency of sample estimates of risk averse stochastic programs

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