Advances in Applied Probability
- Adv. in Appl. Probab.
- Volume 46, Number 1 (2014), 139-167.
On the continuous and smooth fit principle for optimal stopping problems in spectrally negative Lévy models
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).
Adv. in Appl. Probab., Volume 46, Number 1 (2014), 139-167.
First available in Project Euclid: 1 April 2014
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]
Secondary: 60J75: Jump processes
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