On Study Of A Foreign Investor’s Investment With Fluctuations Of Exchange Rate Under Jump-diffusion Environment

The optimal portfolio selection problem is one of the basic problems of financial engineering, received extensive attention at home and abroad. And various extreme events always affect the world’s financial markets in the reality of life, make the asset price fluctuating and even generate discontinuous jump, so jump risk also has a significant impact on the investment decisions of investors. Thus, the problem of optimal portfolio research emphasizes the importance of jump factors increasingly. On the other hand, with the deepening of economic globalization, foreign direct investment has become an important part of investment selection. Hence, foreign direct investors would have to consider the impact of fluctuations of exchange rate on its assets and investment portfolio.This paper studies a foreign investor’s direct investment with two kinds of fluctuations of exchange rate under jump-diffusion environment. First, we obtain the dynamics of asset price denoted by native currency by using Ito formula. Then, under maximizing the expected utility of the terminal wealth, through using HJB equation, the optimal allocation strategy is obtained, and an approximate solution of the optimal dynamic asset allocation is derived. Subsequently, we analyze the impacts of the jump and the fluctuations of exchange rate on the optimal allocation strategy of an investor through a numerical simulation.Secondly, assuming that fluctuations of exchange rate obeying a mean reverting process, by using the above derivation we again obtain the optimal asset allocation of a foreign direct investor, and analyze the impacts of parameters of the jump and the fluctuations of exchange rate on the foreign investor’s direct investment.Finally, we compare the effects of two different fluctuations of exchange rate on foreign direct investment. The results show that when fluctuations of exchange rate is random situation, foreign investors are more willing to invest his assets into risky assets. In the case that fluctuations of exchange rate with a mean reverting process, the foreign direct investors will pay more attention to macro-control policies of the investee country, and adjust the ratio of investment in order to gain maximum benefit.