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.
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Karatzas et al. (2000) studied this question.
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