Convex integral functionals of processes of bounded variation

TL;DR

This paper characterizes conjugates and subdifferentials of convex integral functionals over processes of bounded variation, with implications for stochastic control and finance.

Contribution

It provides new results on the duality and interchange of integration and minimization for BV processes, expanding the theoretical framework.

Findings

Domain of conjugate contained in semimartingales

New interchange results for integration and minimization

Applications in stochastic control and finance

Abstract

This article characterizes conjugates and subdifferentials of convex integral functionals over the linear space $\mathcal N^\infty$ of stochastic processes of essentially bounded variation (BV) when $\mathcal N^\infty$ is identified with the Banach dual of the space of regular processes. Our proofs are based on new results on the interchange of integration and minimization of integral functionals over BV processes. Under mild conditions, the domain of the conjugate is shown to be contained in the space of semimartingales which leads to several applications in the duality theory in stochastic control and mathematical finance.