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

Jiexian Li, Gordan Zitkovic

Published 2015-05-10Version 1

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