Type of Document Dissertation Author Luttamaguzi, Jamiiru Author's Email Address firstname.lastname@example.org URN etd-1218101-120133 Title A Monotone Follower Control Problem with a Nonconvex Functional and Some Related Problems Degree Doctor of Philosophy (Ph.D.) Department Mathematics Advisory Committee
Advisor Name Title Guillermo Ferreyra Committee Chair Amha Lisan Committee Member George Cochran Committee Member Jurgen Hurrelbrink Committee Member Padmanabhan Sundar Committee Member Steven Seiden Dean's Representative Keywords
- monotone follower control
- singular stochastic control
- nonconvex functional
- optimal stopping
Date of Defense 2001-12-12 Availability unrestricted AbstractA 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.
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