IJPAM: Volume 66, No. 3 (2011)

ONE KIND OF OPTIMAL CONTROL PROBLEM OF
PORTFOLIO AND CONSUMPTION CHOICE
WITH POWER UTILITY FUNCTION

Yue Xi$^1$, Chengxin Luo$^2$
$^{1,2}$College of Mathematics and Systems Science
Shenyang Normal University
Shenyang, 110034, P.R. CHINA
$^1$e-mail: xiyue0719@163.com
$^2$e-mail: luochengxin@163.com


Abstract.This paper concerns with one kind of optimal control problem of portfolio and consumption choice in a financial market, in which the investor has three different investments. One is a bond, the other is a stock, and the third is a foreign exchange deposit. Using dynamic programming approach, the explicit optimal portfolio and consumption choice are obtained for the power utility function case.

Received: November 30, 2010

AMS Subject Classification: 93E20, 60G40

Key Words and Phrases: optimal portfolio, Hamilton-Jacobi-Bellman equation, power utility function

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2011
Volume: 66
Issue: 3