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Zbl 0963.93079
Karatzas, Ioannis; Wang, Hui
Utility maximization with discretionary stopping. (English)
[J] SIAM J. Control Optimization 39, No.1, 306-329 (2000). ISSN 0363-0129; ISSN 1095-7138/e

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.
[Klaus Ehemann (Karlsruhe)]

MSC 2000:: *93E20 Optimal stochastic control (systems)
91B16 Utility theory
91B28 Finance etc.
60G40 Optimal stopping
49N15 Duality theory (optimization)

Keywords: utility maximization; stochastic control; optimal stopping; variational inequality; duality; convex analysis; martingale representation; existence of optimal strategies

Cited in: Zbl 1165.60021

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