Advances in Applied Probability

On the continuous and smooth fit principle for optimal stopping problems in spectrally negative Lévy models

Masahiko Egami and Kazutoshi Yamazaki

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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).

Article information

Source
Adv. in Appl. Probab., Volume 46, Number 1 (2014), 139-167.

Dates
First available in Project Euclid: 1 April 2014

Permanent link to this document
https://projecteuclid.org/euclid.aap/1396360107

Digital Object Identifier
doi:10.1239/aap/1396360107

Mathematical Reviews number (MathSciNet)
MR3189052

Zentralblatt MATH identifier
06293579

Subjects
Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]
Secondary: 60J75: Jump processes

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

Citation

Egami, Masahiko; Yamazaki, Kazutoshi. On the continuous and smooth fit principle for optimal stopping problems in spectrally negative Lévy models. Adv. in Appl. Probab. 46 (2014), no. 1, 139--167. doi:10.1239/aap/1396360107. https://projecteuclid.org/euclid.aap/1396360107


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