Reflected BSDEs and optimal control and stopping for infinite-dimensional systems

TL;DR

This paper introduces a new concept of mild supersolutions for obstacle problems in infinite-dimensional spaces, linking them to reflected BSDEs, and applies these results to optimal control and stopping problems.

Contribution

It develops the notion of mild supersolutions for obstacle problems in infinite-dimensional Hilbert spaces and connects them to reflected BSDEs, advancing the theoretical framework.

Findings

Defined mild supersolutions for obstacle problems in Hilbert spaces

Established the minimal supersolution via reflected BSDEs

Applied the framework to optimal control and stopping problems

Abstract

We introduce the notion of mild supersolution for an obstacle problem in an infinite dimensional Hilbert space. The minimal supersolution of this problem is given in terms of a reflected BSDEs in an infinite dimensional Markovian framework. The results are applied to an optimal control and stopping problem.