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


Reference:

Alili, L. and Kyprianou, A. E., 2005. Some remarks on first passage of Levy processes, the American put and pasting principles. Annals of Applied Probability, 15 (3), pp. 2062-2080.

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Official URL:

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Gerber and Shiu [Astin Bull. 24 (1994) 195–220], Boyarchenko and Levendorskiǐ [Working paper series EERS 98/02 (1998), Unpublished manuscript (1999), SIAM J. Control Optim. 40 (2002) 1663–1696], Chan [Original unpublished manuscript (2000)], Avram, Chan and Usabel [Stochastic Process.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

Details

Item Type Articles
CreatorsAlili, L.and Kyprianou, A. E.
DOI10.1214/105051605000000377
DepartmentsFaculty of Science > Mathematical Sciences
RefereedYes
StatusPublished
ID Code7190

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