On a generalization of the Dvoretzky-Wald-Wolfowitz theorem with an application to a robust optimization problem

TL;DR

This paper extends the Dvoretzky-Wald-Wolfowitz theorem to conditional expectations under specific conditions, providing a theoretical foundation for robust optimization applications.

Contribution

It generalizes a classical theorem to a broader setting involving conditional expectations with no conditional atoms.

Findings

The theorem is successfully extended to conditional expectations.

The generalization applies when the sigma-field has no conditional atoms.

Potential applications in robust optimization are discussed.

Abstract

A generalization of the Dvoretzky-Wald-Wolfowitz theorem to the case of conditional expectations is provided assuming that the $\sigma$-field on the state space has no conditional atoms.