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Utility maximization with discretionary stopping. (English) Zbl 0963.93079
This paper regards utility maximization problems of mixed types (optimal stopping and control). These types are reduced to pure optimal stopping problems which are then solved. Sufficient conditions for the existence of optimal strategies are provided. The mathematical tools are optimal stopping, continuous-time martingales, convex analysis, and duality theory. Several examples are given including one demonstrating that optimal strategies need not always exist.

MSC:
93E20 Optimal stochastic control
91B16 Utility theory
91G10 Portfolio theory
60G40 Stopping times; optimal stopping problems; gambling theory
49N15 Duality theory (optimization)
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