Some remarks on first passage of Levy processes, the American put and pasting principles
AbstractThe 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Gerber and Shiu [Astin Bull. 24 (1994) 195-220], Boyarchenko and Levendorskii [Working paper series EERS 98/02 (1998), Unpublished manuscript (1999), SIAM J. Control Optim. 40 (2002) 1663-1696], Chan [Original unpublished manuscript (2000)], Avram, Chan and Usabel [Stochastic Process.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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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number math/0508487.
Date of creation: Aug 2005
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Publication status: Published in Annals of Applied Probability 2005, Vol. 15, No. 3, 2062-2080
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- Ariel Almendral & Cornelis W. Oosterlee, 2007. "On American Options Under the Variance Gamma Process," Applied Mathematical Finance, Taylor and Francis Journals, vol. 14(2), pages 131-152.
- Marc Chesney & M. Jeanblanc, 2004. "Pricing American currency options in an exponential Levy model," Applied Mathematical Finance, Taylor and Francis Journals, vol. 11(3), pages 207-225.
- Ernesto Mordecki, 2002. "Optimal stopping and perpetual options for Lévy processes," Finance and Stochastics, Springer, vol. 6(4), pages 473-493.
- Dayanik, Savas & Sezer, Semih O., 2006. "Sequential testing of simple hypotheses about compound Poisson processes," Stochastic Processes and their Applications, Elsevier, vol. 116(12), pages 1892-1919, December.
- Erhan Bayraktar, 2007. "On the Perpetual American Put Options for Level Dependent Volatility Models with Jumps," Papers math/0703538, arXiv.org, revised Jan 2009.
- Masahiko Egami & Tim S. T. Leung & Kazutoshi Yamazaki, 2011.
"Default Swap Games Driven by Spectrally Negative Levy Processes,"
1105.0238, arXiv.org, revised Sep 2012.
- Egami, Masahiko & Leung, Tim & Yamazaki, Kazutoshi, 2013. "Default swap games driven by spectrally negative Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 123(2), pages 347-384.
- Medvedev, Alexey & Scaillet, Olivier, 2010. "Pricing American options under stochastic volatility and stochastic interest rates," Journal of Financial Economics, Elsevier, vol. 98(1), pages 145-159, October.
- Bo, Lijun & Song, Renming & Tang, Dan & Wang, Yongjin & Yang, Xuewei, 2012. "Lévy risk model with two-sided jumps and a barrier dividend strategy," Insurance: Mathematics and Economics, Elsevier, vol. 50(2), pages 280-291.
- Luis H. R. Alvarez E. & Pekka Matom\"aki & Teppo A. Rakkolainen, 2013.
"A Class of Solvable Optimal Stopping Problems of Spectrally Negative Jump Diffusions,"
- Luis H. R. Alvarez & Teppo A. Rakkolainen, 2006. "A Class of Solvable Optimal Stopping Problems of Spectrally Negative Jump Diffusions," Discussion Papers 9, Aboa Centre for Economics.
- Rama Cont & Cecilia Mancini, 2010. "Nonparametric tests for pathwise properties of semimartingales," DiMaD Working Papers 2010-02, Dipartimento di Matematica per le Decisioni, Universita' degli Studi di Firenze.
- Pavel V. Gapeev, 2006. "Perpetual Barrier Options in Jump-Diffusion Models," SFB 649 Discussion Papers SFB649DP2006-058, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
- Gapeev, Pavel V., 2008. "The integral option in a model with jumps," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2623-2631, November.
- Christensen, Sören & Salminen, Paavo & Ta, Bao Quoc, 2013. "Optimal stopping of strong Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 1138-1159.
- Erhan Bayraktar, 2007. "A Proof of the Smoothness of the Finite Time Horizon American Put Option for Jump Diffusions," Papers math/0703782, arXiv.org, revised Dec 2008.
- Christensen, Sören & Irle, Albrecht, 2009. "A note on pasting conditions for the American perpetual optimal stopping problem," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 349-353, February.
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