Optimize Expected Utility From Terminal Wealth And Consumption With Transaction Costs

This paper solves the problem of an agent who begins with an initial endowment and who can consume while also investing in a standard complete market with transaction costs. Let f(t) be proportional function of transaction costs ,we set up the investment consumption model of coninuous time. We get the optimal investment consumption process and terminal wealth by using the convex dual function (Legendre transform) of the utility function and the theory of martingal. It proves that active exchange don't improve the expected terminal wealth in the viable markets.