A computational scheme for optimal investment - consumption with proportional transaction costs

We consider the optimal investment - consumption strategy of an investor who can invest in a stock and a bank. We consider the case where proportional transaction costs are present and the objective is to maximize the discounted utility of consumption. We describe an efficient computational scheme that transforms the arising free-boundary problem to a sequence of fixed-boundary problems. We prove the convergence of the scheme and also show that the converged solution is the optimal value function. Finally, we compare and contrast the results obtained by our procedure with certain well-known results and approximations. The proposed scheme also lends itself to optimizing portfolios with multiple risky assets.