On the investment-consumption model with transaction costs
Abstract
This paper considers the optimal consumption and investment policy for an investor who has avaible one bank account paying a fixed interest rate r and n risky assets whose prices are log-normal diffusions. We suppose that transactions between the assets incur a cost proportional tothe size of the transaction. The problem is to maximize the total utility of consumption. Dynamic programming leads to a 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.