Optimal Control with Diminishing and Zero Cost for Control

摘要

Research under this grant focused on singular and bang-bang stochastic control and singular deterministic control. The investigators established the connections between a general Monotone Follower problem and a stopping problem: the spatial derivative of the value function of the Monotone Follower problem is the optimal risk function from the stopping problem. Similar results were obtained for the general Reflected Follower problem. This connection between singular control and optimal stopping has proved useful in establishing optimal stopping times via the corresponding control problem and permits application of analytical and numerical methods from optimal stopping to singular control problems. Nine papers were published under this grant, including Connections between optimal stopping and singular stochastic control I, Trivariate density of Brownian motion, its local and occupation time, with application to stochastic control, and A stochastic control problem with different value functions for singular and absolutely continuous control.