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Consistency of sample estimates of risk averse stochastic programs. (English) Zbl 1301.62045

Summary: 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.

MSC:

62G20 Asymptotic properties of nonparametric inference
60F15 Strong limit theorems
90C15 Stochastic programming
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References:

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