Nonconcave Robust Optimization with Discrete Strategies under Knightian Uncertainty

TL;DR

This paper investigates non-concave robust stochastic optimization problems with discrete strategies under Knightian uncertainty, establishing conditions for the existence of solutions in complex, multi-period settings.

Contribution

It introduces new conditions ensuring the existence of maximizers in non-concave, discrete-strategy robust optimization problems under Knightian uncertainty.

Findings

Existence of maximizers under specified conditions

Applicable to optimal stopping and semi-static trading problems

Extends robust optimization theory to non-concave, discrete strategies

Abstract

We study robust stochastic optimization problems in the quasi-sure setting in discrete-time. The strategies in the multi-period-case are restricted to those taking values in a discrete set. The optimization problems under consideration are not concave. We provide conditions under which a maximizer exists. The class of problems covered by our robust optimization problem includes optimal stopping and semi-static trading under Knightian uncertainty.