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Mathematical Problems in Engineering
Volume 2010, Article ID 472867, 16 pages
Research Article

An Application of Dynamic Programming Principle in Corporate International Optimal Investment and Consumption Choice Problem

School of Mathematics, Shandong University, Jinan 250100, China

Received 5 August 2010; Revised 16 December 2010; Accepted 27 December 2010

Academic Editor: Gradimir V. Milovanović

Copyright © 2010 Zongyuan Huang and Zhen Wu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper is concerned with a kind of corporate international optimal portfolio and consumption choice problems, in which the investor can invest her or his wealth either in a domestic bond (bank account) or in an oversea real project with production. The bank pays a lower interest rate for deposit and takes a higher rate for any loan. First, we show that Bellman's dynamic programming principle still holds in our setting; second, in terms of the foregoing principle, we obtain the investor's optimal portfolio proportion for a general maximizing expected utility problem and give the corresponding economic analysis; third, for the special but nontrivial Constant Relative Risk Aversion (CRRA) case, we get the investors optimal investment and consumption solution; last but not least, we give some numerical simulation results to illustrate the influence of volatility parameters on the optimal investment strategy.