Benefits of Fluctuating Exchange Rates on the Investor's Wealth

We consider a problem of maximizing the utility of an agent who invests in a stock and a money market account incorporating proportional transaction costs $\left(\lambda >0\right)$ and foreign exchange rate fluctuations. Assuming a HARA utility function $U\left(c\right)=c^p/p$ for all $c\ge 0$ , $p<1$ , $p\ne 0$ , we suggest an approach of determining the value function. Contrary to fears associated with exchange rate fluctuations, our results show that these fluctuations can bring about tangible benefits in one’s wealth. We quantify the level of these benefits. We also present an example which illustrates an investment strategy of our agent.