# Asymptotics of minimax stochastic programs

*Alexander Shapiro* ()

*Statistics & Probability Letters*, 2008, vol. 78, issue 2, 150-157

**Abstract:**
We discuss in this paper asymptotics of the sample average approximation (SAA) of the optimal value of a minimax stochastic programming problem. The main tool of our analysis is a specific version of the infinite dimensional delta method. As an example, we discuss asymptotics of SAA of risk averse stochastic programs involving the absolute semideviation risk measure. Finally, we briefly discuss exponential rates of convergence of the optimal value of SAA problems.

**Keywords:** Sample; average; approximation; Infinite; dimensional; delta; method; Functional; central; limit; theorem; Minimax; stochastic; programming; Absolute; semideviation; risk; measure; Exponential; rate; of; convergence (search for similar items in EconPapers)

**Date:** 2008

**References:** View complete reference list from CitEc

**Citations:** View citations in EconPapers (5) Track citations by RSS feed

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