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On the continuous and smooth fit principle for optimal stopping problems in spectrally negative Lévy models. (English) Zbl 1398.60062

Summary: We consider a class of infinite time horizon optimal stopping problems for spectrally negative Lévy processes. Focusing on strategies of threshold type, we write explicit expressions for the corresponding expected payoff via the scale function, and further pursue optimal candidate threshold levels. We obtain and show the equivalence of the continuous/smooth fit condition and the first-order condition for maximization over threshold levels. As examples of its applications, we give a short proof of the McKean optimal stopping problem (perpetual American put option) and solve an extension to [the authors, Stochastics 85, No. 1, 111–143 (2013; Zbl 1288.91187)].

MSC:

60G40 Stopping times; optimal stopping problems; gambling theory
60J75 Jump processes (MSC2010)
91G40 Credit risk

Citations:

Zbl 1288.91187
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References:

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