# Convex integral functionals of cadlag processes

## TL;DR

This paper develops a general convex duality framework for integral functionals of cadlag processes, enabling applications in optimal stopping, stochastic control, and finance through new measurability and interchange results.

## Contribution

It introduces new measurability results and interchange rules for convex integral functionals on cadlag processes, advancing the theoretical foundation for stochastic optimization.

## Key findings

- Characterizes conjugates and subdifferentials of convex integral functionals.
- Provides a unified approach to convex duality in stochastic process optimization.
- Enables applications in optimal stopping, control, and finance.

## Abstract

This article characterizes conjugates and subdifferentials of convex integral functionals over linear spaces of cadlag stochastic processes. The approach is based on new measurability results on the Skorokhod space and new interchange rules of integral functionals that are developed in the article. The main results provide a general approach to apply convex duality in a variety of optimization problems ranging from optimal stopping to singular stochastic control and mathematical finance.