Martingale and Relaxation-Projection Methods for Utility Maximization with Portfolio Constraints and Stochastic Income

Yunhong Yang

The problem of maximizing the expected utility from terminal wealth in the presence of a stochastic endowment and constraints on the portfolio choices is examined. We model short-sale and borrowing constraints, as well as incomplete markets, as special cases of constraints. The existence of optimal policies is established under fairly general assumptions on the security price coefficients and the individual's utility function. This result is obtained by using martingale techniques to reformulate the individual's dynamic optimization problem as an equivalent static one.