Title page for ETD etd-1218101-120133


Type of Document Dissertation
Author Luttamaguzi, Jamiiru
Author's Email Address jamiiru@excite.com
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
Abstract
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.

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