Abstract
We consider an agent who does not consume and who invests all the wealth in a money market and in several stocks. We assume that he pays proportional transaction costs for each trade and that he wants to maximize the long run growth rate of the certainty equivalent of the wealth process provided that the stock market prices follow a multidimensional geometric Brownian motion provided that he faces HARA utility function unbounded from below.
We assume that the investor is interested in an almost optimal strategy for small transaction taxes. This leads us to a certain partial differential equation, which can be solved explicitly in the case where the stock prices are independent.
Thus we are able to propose a strategy that should be almost optimal for small values of transaction taxes in case of independent stocks.