Doctor of Philosophy (PhD)
A generalized one-dimensional monotone follower control problem with a nonconvex functional is considered. The controls are assumed to be nonnegative progressively measurable processes. The verification theorem for this problem is presented. A specific monotone follower control problem with a nonconvex functional is then considered in which the diffusion term is constant. The optimal control for this problem, which is explicitly given, can be viewed as tracking a standard Wiener process by a non anticipating process starting at 0. For some parameters values, the value function for this monotone follower control problem is shown to be C2 and for other values it is shown not to be C2. Next, a singular control problem with constant coefficients and bounded controls appearing in both the drift and diffusion terms is shown to be equivalent to an optimal stopping problem. Lastly, other various singular control problems are considered for both smoothness of their value functions and existence of their optimal control processes.
Document Availability at the Time of Submission
Release the entire work immediately for access worldwide.
Luttamaguzi, Jamiiru, "A monotone follower control problem with a nonconvex functional and some related problems" (2002). LSU Doctoral Dissertations. 2603.