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1 results

  • Consistency of Sample Estimates of Risk Averse Stochastic Programs

  • Part of
  • Alexander Shapiro
  • Journal:
    Journal of Applied Probability / Volume 50 / Issue 2 / June 2013
    Published online by Cambridge University Press:
    30 January 2018, pp. 533-541
    Print publication:
    June 2013
    • Article
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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.