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I will consider the problem of optimally allocating wealth among multiple stock and a bank account, in order to maximize the infinite horizon discounted utility of consumption. When it is possible to transfer wealth from one asset to another without incurring transaction costs, the optimal solution was found by Merton. I consider the situation where the transfer of wealth from one asset to another involves transaction costs that are proportional to the amount of wealth transferred. I will first describe/construct the model as a stochastic control problem with both continuous and singular controls. Then I will present an efficient numerical method to solve this problem. Then using this method I will study the impact of volatity, risk aversion of the investor, the level of transaction costs and the correlation structure on the optimal policy. |
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