IJPAM: Volume 57, No. 4 (2009)

UTILITY MAXIMIZATION WITH PARTIAL
INFORMATION FOR ORNSTEIN-UHLENBECK MODEL

Fangfang Liu$^1$, Chengxin Luo$^2$
$^{1,2}$College of Mathematics and System Science
Shenyang Normal University
Shenyang, 110034, P.R. CHINA
$^1$e-mail: liufangfang0302@163.com
$^2$e-mail: luochengxin@163.com


Abstract.This paper deals with a class of stochastic optimization and consumption models for the exponential utility, which is maximizing the expected utility of the terminal wealth and intermediate consumption. The stock price is modelled as a stochastic differential equation with instantaneous rates of return modelled as an Ornstein-Uhlenbeck process. Only the stock price and interest rate can be observable for an investor. It is reduced to a partially observed stochastic control problem. Combining the filtering theory with the dynamic programming approach, corresponding optimal strategies are derived.

Received: November 11, 2009

AMS Subject Classification: 93E20, 91B28, 93E11

Key Words and Phrases: Hamilton-Jacobi-Bellman (HJB) equation, utility maximization, filtering theory

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 57
Issue: 4