Research on Investment-Consumption Problem with Proportional Transaction Costs

Investment consumption problem with proportional transaction costs is researched in this paper by the method of non-singular stochastic optimal control. It is easy to obtain buying, selling and no transaction regions in the solvency region and corresponding optimal buying, selling and consumption policies, because the expressions of the optimization problem obtained from this method is quadratic. Optimal buying, selling and consumption policies are obtained explicitly in this paper, since the investor's utility is homothetic