Optimum Consumption and Portfolio Selection with Transaction Costs

(Abstract)

When considering the optimal consumption and investment decisions for an investor, suppose the "geometric Brownian motion" hypothesis holds in perfect markets. Assume the investor has available a bank account paying a fixed rate of interest and a stock whose price is a log-normal diffusion. Suppose that there are charges on all transactions equal to a fixed percentage of the amount transacted. It is then shown that the optimal buying and selling policies are the local times of the two-dimensional process of bank and stock holdings at the boundaries of a wedge-shaped region which is determined by the solution of a nonlinear free boundary problem.