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We study the classical problem of allocation of funds between a bank account which grows with a deterministic rate and of a risky asset such as a stock whose value follows a geometric Brownian motion with a drift. We maximize the expected rate of growth of the net wealth in the presence of proportional transaction costs when transactions are made between the two assets. Our optimal strategy strategy keeps the ratio of the values of these assets in an interval with minimum control. Finally an application of the model to a real stock is presented.

Optimal portfolio allocation for long-term growth of wealth in the presence of transaction costs