Connections between Optimal Stopping and Singular Stochastic Control I. Monotone Follower Problems
Ioannis Karatzas, Steven E. Shreve · SIAM Journal on Control and Optimization · 1984
The stochastic control problem of tracking a Brownian motion by a nondecreasing process (Monotone Follower) is related to a question of Optimal Stopping. Direct probabilistic arguments are employed to show that the two problems are equivalent, and that both admit optimal solutions.