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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:
93E20Optimal stochastic control (systems)
91B16Utility theory
91B28Finance etc. (MSC2000)
60G40Stopping times; optimal stopping problems; gambling theory
49N15Duality theory (optimization)