## Journal of Applied Probability

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

### 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 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