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

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

2005-08-25

arxiv.org/abs/math/0508487v1

Annals of Applied Probability 2005, Vol. 15, No. 3, 2062-2080

Mathematics

Probability

Published at http://dx.doi.org/10.1214/105051605000000377 in the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

10.1214/105051605000000377

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Gerber and Shiu [Astin Bull. 24 (1994) 195-220], Boyarchenko and Levendorskii [Working paper series EERS 98/02 (1998), Unpublished manuscript (1999), SIAM J. Control Optim. 40 (2002) 1663-1696], Chan [Original unpublished manuscript (2000)], Avram, Chan and Usabel [Stochastic Process.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