IJPAM: Volume 55, No. 2 (2009)
RANDOM FINAL TIME
Department of Mathematics and Industrial Engineering
École Polytechnique
C.P. 6079, Succursale Centre-Ville
Montreal, Quebec, H3C 3A7, CANADA
e-mail: mlefebvre@polymtl.ca
Abstract.Problems involving controlled one-dimensional diffusion processes
over a random time interval are considered. The infinitesimal
variance of the processes depends on the control variable. The
processes are controlled until they leave the interval
.
The cost criterion whose expected value we want to minimize is such
that, in addition to the quadratic control costs, a final cost is
incurred if
, where
is the random final
time. Exact and explicit solutions are obtained in special cases
both for the optimal control and for the value function. A related
game theory problem is also presented.
Received: February 11, 2007
AMS Subject Classification: 93E20, 49N70
Key Words and Phrases: LQG homing, Brownian motion, hitting time, game theory
Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 55
Issue: 2