Connections Between Optimal Stopping and Singular Stochastic Control II. Reflected Follower Problems
Ioannis Karatzas, Steven E. Shreve · SIAM Journal on Control and Optimization · 1985
The stochastic control problem of following a Brownian path by a process of bounded variation, and subject to a reflecting barrier at the origin (reflected follower), is reduced to a question of optimal stopping with absorption. Direct probabilistic arguments are used to establish the equivalence of the two problems under suitable conditions on the cost functions.