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March 2014 On the continuous and smooth fit principle for optimal stopping problems in spectrally negative Lévy models
Masahiko Egami, Kazutoshi Yamazaki
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Adv. in Appl. Probab. 46(1): 139-167 (March 2014). DOI: 10.1239/aap/1396360107

Abstract

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 Egami and Yamazaki (2013).

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Masahiko Egami. Kazutoshi Yamazaki. "On the continuous and smooth fit principle for optimal stopping problems in spectrally negative Lévy models." Adv. in Appl. Probab. 46 (1) 139 - 167, March 2014. https://doi.org/10.1239/aap/1396360107

Information

Published: March 2014
First available in Project Euclid: 1 April 2014

zbMATH: 06293579
MathSciNet: MR3189052
Digital Object Identifier: 10.1239/aap/1396360107

Subjects:
Primary: 60G40
Secondary: 60J75

Keywords: continuous and smooth fit , Optimal stopping , scale function , spectrally negative Lévy process

Rights: Copyright © 2014 Applied Probability Trust

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Vol.46 • No. 1 • March 2014
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