Existence, Characterization and Approximation in the Generalized Monotone-Follower Problem

TL;DR

This paper extends the classical monotone-follower problem by using advanced mathematical tools to establish existence, approximation, and deepen the understanding of its connection to stochastic control and stopping problems.

Contribution

It introduces a generalized formulation of the monotone-follower problem and applies Meyer-Zheng weak convergence and Pontryagin's maximum principle to derive new theoretical results.

Findings

Existence of solutions under weak conditions

General approximation results for the problem

Deeper understanding of the link between stochastic control and stopping

Abstract

We revisit the classical monotone-follower problem and consider it in a generalized formulation. Our approach is based on a compactness substitute for nondecreasing processes, the Meyer-Zheng weak convergence, and the maximum principle of Pontryagin. It establishes existence under weak conditions, produces general approximation results and further elucidates the celebrated connection between singular stochastic control and stopping.