Journal of Applied Probability

Consistency of sample estimates of risk averse stochastic programs

Alexander Shapiro

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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.

Article information

J. Appl. Probab., Volume 50, Number 2 (2013), 533-541.

First available in Project Euclid: 19 June 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62F12: Asymptotic properties of estimators
Secondary: 90C15: Stochastic programming

Law invariant convex and coherent risk measures stochastic programming law of large numbers consistency of statistical estimators epiconvergence sample average approximation


Shapiro, Alexander. Consistency of sample estimates of risk averse stochastic programs. J. Appl. Probab. 50 (2013), no. 2, 533--541. doi:10.1239/jap/1371648959.

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