Journal of Applied Probability

The smooth-fit property in an exponential Lévy model

Damien Lamberton and Mohammed Mikou

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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

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

First available in Project Euclid: 8 March 2012

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Optimal stopping Lévy process smooth-fit property American option


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.

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