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

By L. Alili, Andreas E. Kyprianou. 2005

232 citations recorded by the source corpus.

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Gerber and Shiu [Astin Bull. 24 (1994) 195–220], Boyarchenko and Levendorskii [Working paper series EERS 98/02 (1998), Unpublished manuscript (1999), SIAM J. Control Optim. 40 (2002) 1663–1696], Chan [Original unpublished manuscript (2000)], Avram, Chan and Usabel [Stochastic Process.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

Subfields: Finance, Management Information Systems, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/7a0f8ddd3fec0e19832634e835d87cb34788a0ce

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Citations in the corpus

On American Options Under the Variance Gamma Process (2007, background): “In this paper, we prove facts about the behavior of the free boundary and in particular about the failure of the smooth fit principle for American options under the VG process; see also [1, 4, 5, 19].”
A Wiener–Hopf Monte Carlo simulation technique for Lévy processes (2009, unknown): “Jan. 2021 The Annals of Applied Probability 2011, Vol. 21, No. 6, 2171–2190 DOI: 10.1214/10-AAP746 © Institute of Mathematical Statistics, 2011”
Nonparametric tests for pathwise properties of semimartingales (2011, background): “Even within the class of purely discontinuous models, one finds a variety of models with different path properties – finite/infinite jump intensity, finite/infinite variation – which turn out to have an importance in applications, such as optimal stopping [5] and the asymptotic behavior of option pr”
Exact joint laws associated with spectrally negative Lévy processes and applications to insurance risk theory (2011, background): “Furthermore, c(1 − Ψ(0)) = EX(1) = φ(Φ(q)).”
Discounted Optimal Stopping for Maxima of Some Jump-Diffusion Processes (2007, background): “The key point to note when solving optimal stopping problems for the jump processes established in [27] and [28] is that the smooth-fit condition at the optimal boundary may break down and then needs replacing by the continuous-fit condition; see also [1] for necessary and sufficient conditions for ”
The McKean stochastic game driven by a spectrally negative Lévy process (2008, unknown): “Firstly, as was already found in numerous papers concerning optimal stopping problems driven by spectrally one sided Lévy processes (cf. Alili and Kyprianou (2005), Chan (2004) and Avram et al. (2004)), smooth pasting breaks down when the Lévy process is of bounded variation.”
Old and New Examples of Scale Functions for Spectrally Negative Levy Processes (2007, background): “For example, in the theory of optimal stopping Avram et al. (2002, 2004); Alili and Kyprianou (2005) and Kyprianou (2006), in the theory of optimal control Avram et al. (2007) and Loeffen (2007), in the theory of queuing and storage models Dube et al. (2004) and Bekker et al. (2007), in the theory…”