Stochastic programs without duality gaps

TL;DR

This paper investigates conditions ensuring the existence of solutions and no duality gaps in dynamic stochastic optimization problems, with applications in finance and operations research, using extended dynamic programming under relaxed no-arbitrage conditions.

Contribution

It introduces new relaxed conditions for extended dynamic programming that guarantee solution existence and duality gap absence in stochastic optimization.

Findings

Sufficient conditions for solution existence

Conditions ensuring no duality gap

Generalization of no-arbitrage conditions

Abstract

This paper studies dynamic stochastic optimization problems parametrized by a random variable. Such problems arise in many applications in operations research and mathematical finance. We give sufficient conditions for the existence of solutions and the absence of a duality gap. Our proof uses extended dynamic programming equations, whose validity is established under new relaxed conditions that generalize certain no-arbitrage conditions from mathematical finance.