Annals of Applied Probability

Some remarks on first passage of Lévy processes, the American put and pasting principles

L. Alili and A. E. Kyprianou

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The purpose of this article is to provide, with the help of a fluctuation identity, a generic link between a number of known identities for the first passage time and overshoot above/below a fixed level of a Lévy process and the solution of Gerber and Shiu [Astin Bull. 24 (1994) 195–220], Boyarchenko and Levendorskiǐ [Working paper series EERS 98/02 (1998), Unpublished manuscript (1999), SIAM J. Control Optim. 40 (2002) 1663–1696], Chan [Original unpublished manuscript (2000)], Avram, Chan and Usabel [Stochastic Process. Appl. 100 (2002) 75–107], Mordecki [Finance Stoch. 6 (2002) 473–493], Asmussen, Avram and Pistorius [Stochastic Process. Appl. 109 (2004) 79–111] and Chesney and Jeanblanc [Appl. Math. Fin. 11 (2004) 207–225] to the American perpetual put optimal stopping problem. Furthermore, we make folklore precise and give necessary and sufficient conditions for smooth pasting to occur in the considered problem.

Article information

Ann. Appl. Probab., Volume 15, Number 3 (2005), 2062-2080.

First available in Project Euclid: 15 July 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]
Secondary: 60J75: Jump processes 91B70: Stochastic models 60G51: Processes with independent increments; Lévy processes

Optimal stopping American options principle of smooth pasting principle of continuous pasting Lévy processes


Alili, L.; Kyprianou, A. E. Some remarks on first passage of Lévy processes, the American put and pasting principles. Ann. Appl. Probab. 15 (2005), no. 3, 2062--2080. doi:10.1214/105051605000000377.

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