Journal of Applied Probability

Consistency of sample estimates of risk averse stochastic programs

Alexander Shapiro

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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 sample-based estimators of risk averse stochastic programming problems.

Article information

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

Dates
First available in Project Euclid: 19 June 2013

Permanent link to this document
https://projecteuclid.org/euclid.jap/1371648959

Digital Object Identifier
doi:10.1239/jap/1371648959

Mathematical Reviews number (MathSciNet)
MR3102498

Zentralblatt MATH identifier
1301.62045

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

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

Citation

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. https://projecteuclid.org/euclid.jap/1371648959


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