Defense March 25, 1999 Finite Time Horizon Portfolio Optimization Problems with Transaction Costs This dissertation examines the optimal portfolio selection problem on a finite time horizon, with a single back account and multiple stock portfolio, taking into consideration proportional transaction costs. Given the initial time and the initial position of the investor, the problem is to determine a consumption and investment strategy which will maximize the expected value of a given objective function of the total consumption and the terminal wealth. The principle of dynamic programming is proven and used to determine the Hamilton-Jacobi-Bellman (HJB) equation. For this problem, the HJB is a variational inequality that involves a non-linear parabolic partial differential equation with free boundaries that are described by several linear partial differential equations. It is shown that the value function satisfies the HJB equation in the viscosity sense. The optimal trading and consumption strategy is provided for a specific type of objective function under certain assumptions.