An algorithm for optimal portfolio selection problem with transaction costs and random lifetimes

We study a consumption and portfolio selection problem in the presence of proportional transaction costs. In order to explore the effects of the expectation about the length of an investor’s lifetime on her optimal consumption and investment, we generalize Constantinides’ [2] optimal investment model with transaction costs by randomizing the investor’s lifetime. We convert the problem into a free boundary problem with two free boundaries and obtain an optimal consumption and investment policy. We provide a numerical algorithm for this free boundary problem and prove convergence of a numerical solution obtained by the algorithm to a true solution. By using numerical results, we investigate the effect of investor’s expected lifetime on liquidity premia due to transaction costs.