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Optimal stopping with random horizon. (Spanish. English summary) Zbl 0734.60045

Summary: We analyze the optimal stopping problem with random horizon in Markov processes with continuous time. We study the case whose horizon is a first entrance time in the interior of B, a closed set. The B-excessive functions are defined and we show these functions coincide with the payoff of the stopping problem. Then we introduce several sets which permit us to characterize the stopping domains. Finally we show the explicit form of some of these domains when the process is a Brownian motion.

MSC:

60G40 Stopping times; optimal stopping problems; gambling theory
60J25 Continuous-time Markov processes on general state spaces
60J65 Brownian motion
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References:

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