Optimal stopping, randomized stopping and singular control with partial information flow

TL;DR

This paper extends the relationship between optimal stopping, randomized stopping, and singular control to scenarios with general information flows, introducing a new framework for partial information problems and their solutions via variational inequalities.

Contribution

It generalizes the classical connection between stopping and control problems to settings with arbitrary information flows, using variational inequalities for solutions.

Findings

Established equivalence between partial information stopping and singular control.

Introduced a variational inequality framework for partial information control problems.

Extended Krylov's ideas to more general information structures.

Abstract

The purpose of this paper is two-fold: We extend the well-known relation between optimal stopping and randomized stopping of a given stochastic process to a situation where the available information flow is a filtration with no a priori assumed relation to the filtration of the process. We call these problems optimal stopping and randomized stopping with general information. Following an idea of Krylov [K] we introduce a special singular stochastic control problem with general information and show that this is also equivalent to the partial information optimal stopping and randomized stopping problems. Then we show that the solution of this singular control problem can be expressed in terms of partial information variational inequalities.