Study of Constrained Portfolio Model on Optimization of Utility from Terminal Wealth

The present paper studies the stochastic control problem of maximizing expected utility from terminal wealth, when portfolio is constrained to take values in a given closed, convex subset of R^d.Equivalent conditions for optimality are obtained. Existence theorem for optimal portfolio is provided. On condition to deterministic coefficients, optimal portfolio formulae in feedback is given, and a simple example is discussed.