Utility Maximization with Discretionary Stopping

Utility maximization problems of mixed optimal stopping /control type are considered, which can be solved by reduction to a family of related pure optimal stopping problems. Sufficient conditions for the existence of optimal strategies are provided in the context of continuous-time, Itô process models for complete markets. The mathematical tools used are those of optimal stopping theory, continuous-time martingales, convex analysis and duality theory. Several examples are solved explicitly, including one which demonstrates that optimal strategies need not always exist. SIAM Journal on Control & Optimization, to appear. AMS 1991 Subject Classifications: Primary 93E20, 90A09, 60H30; Secondary 60G44, 49N15, 90A16.