On an Investment-Consumption Model with Transaction Costs

On an investment-consumption model with transaction costs, SIAM J. Abstract. This paper considers the optimal consumption and investment policy for an investor who has available one bank account paying a fixed interest rate and n risky assets whose prices are log-normal diffusions. We suppose that transactions between the assets incur a cost proportional to the size of the transaction. The problem is to maximize the total utility of consumption. Dynamic programming leads to a variational inequality for the value function. Existence and uniqueness of a viscosity solution are proved. The variational inequality is solved by using a numerical algorithm based on policies, iterations, and multigrid methods. Numerical results are displayed for n 1 and n-2. 1. Introduction. This paper concerns the theoretical and numerical study of a portfolio selection problem. Consider an investor who has available one riskless bank account paying a fixed rate of interest r and n risky assets modeled by log-normal