Consistency of sample estimates of risk averse stochastic programs

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 samplebased estimators of risk averse stochastic programming problems © 2013 Applied Probability Trust.