Journal of Applied Probability

The smooth-fit property in an exponential Lévy model

Damien Lamberton and Mohammed Mikou

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Abstract

We study the smooth-fit property of the American put price with finite maturity in an exponential Lévy model when the underlying stock pays dividends at a continuous rate. As in the perpetual case, a regularity property is sufficient for smooth fit to occur. We also derive conditions on the Lévy measure under which smooth fit fails.

Article information

Source
J. Appl. Probab., Volume 49, Number 1 (2012), 137-149.

Dates
First available in Project Euclid: 8 March 2012

Permanent link to this document
https://projecteuclid.org/euclid.jap/1331216838

Digital Object Identifier
doi:10.1239/jap/1331216838

Mathematical Reviews number (MathSciNet)
MR2952886

Zentralblatt MATH identifier
1236.91134

Subjects
Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 60G51: Processes with independent increments; Lévy processes 91G20: Derivative securities
Secondary: 60J75: Jump processes

Keywords
Optimal stopping Lévy process smooth-fit property American option

Citation

Lamberton, Damien; Mikou, Mohammed. The smooth-fit property in an exponential Lévy model. J. Appl. Probab. 49 (2012), no. 1, 137--149. doi:10.1239/jap/1331216838. https://projecteuclid.org/euclid.jap/1331216838


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