Convex duality in stochastic programming and mathematical finance

TL;DR

This paper develops a unified duality framework for convex stochastic programming problems, bridging operations research and mathematical finance, enabling broader application and gap closure in duality analysis.

Contribution

It introduces a general duality framework that unifies existing methods and extends duality results to a wider class of stochastic convex problems.

Findings

Unified duality framework for stochastic convex problems

Extension of duality techniques from finance and operations research

Closure of duality gap in challenging scenarios

Abstract

This paper proposes a general duality framework for the problem of minimizing a convex integral functional over a space of stochastic processes adapted to a given filtration. The framework unifies many well-known duality frameworks from operations research and mathematical finance. The unification allows the extension of some useful techniques from these two fields to a much wider class of problems. In particular, combining certain finite-dimensional techniques from convex analysis with measure theoretic techniques from mathematical finance, we are able to close the duality gap in some situations where traditional topological arguments fail.