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August 2005 Some remarks on first passage of Lévy processes, the American put and pasting principles
L. Alili, A. E. Kyprianou
Ann. Appl. Probab. 15(3): 2062-2080 (August 2005). DOI: 10.1214/105051605000000377

Abstract

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Gerber and Shiu [Astin Bull. 24 (1994) 195–220], Boyarchenko and Levendorskiǐ [Working paper series EERS 98/02 (1998), Unpublished manuscript (1999), SIAM J. Control Optim. 40 (2002) 1663–1696], Chan [Original unpublished manuscript (2000)], Avram, Chan and Usabel [Stochastic Process.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.

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L. Alili. A. E. Kyprianou. "Some remarks on first passage of Lévy processes, the American put and pasting principles." Ann. Appl. Probab. 15 (3) 2062 - 2080, August 2005. https://doi.org/10.1214/105051605000000377

Information

Published: August 2005
First available in Project Euclid: 15 July 2005

zbMATH: 1083.60034
MathSciNet: MR2152253
Digital Object Identifier: 10.1214/105051605000000377

Subjects:
Primary: 60G40
Secondary: 60G51 , 60J75 , 91B70

Keywords: American options , Lévy processes , Optimal stopping , principle of continuous pasting , principle of smooth pasting

Rights: Copyright © 2005 Institute of Mathematical Statistics

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Vol.15 • No. 3 • August 2005
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