Abstract
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.
Highlights
International portfolio diversification problem plays an important role in finance and generally depends on several factors such as barriers of international capital markets, uncertainty of operational cash flows, and the effect of exchange risk on corporate international investment
Equation, we could construct an optimal control for the problem 2.11 - 2.12. This is called the verification technique, which is the chief method to solve this kind of optimization problems using dynamic programming principle
We will take a typical utility function CRRA case to get the explicit solution to the optimal portfolio choice and give the simulation to show the influence of the variability parameters in the market
Summary
International portfolio diversification problem plays an important role in finance and generally depends on several factors such as barriers of international capital markets, uncertainty of operational cash flows, and the effect of exchange risk on corporate international investment. We are concerned with a kind of optimal international corporate portfolio and domestic consumption choice problem. The investor can borrow money from the bank to invest in the real project if he pays higher loan rate than deposit, the investor is supposed to retain her/his domestic consumption habit This reflects an implicit assumption according to which all the foreign projects are evaluated in foreign currency and converted by uncertain exchange rate. In order to maximize her/his expected utility of both consumption and her/his terminal wealth in domestic currency numeraire, the problem is formulated as a kind of optimal control problems To deal with this kind of problems, an efficient method is to apply Bellman’s dynamic programming principle which was originally founded in 1952 see Bellman 9.
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