IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v126y2016i4p1124-1144.html
   My bibliography  Save this article

On exact sampling of the first passage event of a Lévy process with infinite Lévy measure and bounded variation

Author

Listed:
  • Chi, Zhiyi

Abstract

Exact sampling of the first passage event (FPE) of a Lévy process with infinite Lévy measure is challenging due to lack of analytic formulas. We present an approach to the sampling for processes with bounded variation. The idea is to embed a process for which we wish to sample the FPE into another process whose FPE can be sampled based on analytic formulas, and once the latter FPE is sampled, extract from it the part belonging to the former process. We obtain general procedures to sample the FPE across a regular nonincreasing boundary or out of an interval. Concrete algorithms are given for two important classes of Lévy processes. The approach is based on distributional results that appear to be new.

Suggested Citation

  • Chi, Zhiyi, 2016. "On exact sampling of the first passage event of a Lévy process with infinite Lévy measure and bounded variation," Stochastic Processes and their Applications, Elsevier, vol. 126(4), pages 1124-1144.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:4:p:1124-1144
    DOI: 10.1016/j.spa.2015.11.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414915002616
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2015.11.001?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Irmingard Eder & Claudia Kluppelberg, 2009. "The first passage event for sums of dependent L\'evy processes with applications to insurance risk," Papers 0912.1925, arXiv.org.
    2. Devroye, Luc & Fawzi, Omar, 2010. "Simulating the Dickman distribution," Statistics & Probability Letters, Elsevier, vol. 80(3-4), pages 242-247, February.
    3. Bertoin, J. & van Harn, K. & Steutel, F. W., 1999. "Renewal theory and level passage by subordinators," Statistics & Probability Letters, Elsevier, vol. 45(1), pages 65-69, October.
    4. Veillette, Mark & Taqqu, Murad S., 2010. "Using differential equations to obtain joint moments of first-passage times of increasing Lévy processes," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 697-705, April.
    5. L. Alili & A. E. Kyprianou, 2005. "Some remarks on first passage of Levy processes, the American put and pasting principles," Papers math/0508487, arXiv.org.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Shantanu Awasthi & Indranil SenGupta, 2020. "First exit-time analysis for an approximate Barndorff-Nielsen and Shephard model with stationary self-decomposable variance process," Papers 2006.07167, arXiv.org, revised Jan 2021.
    2. Boyarchenko, Svetlana & Levendorskii[caron], Sergei, 2007. "Optimal stopping made easy," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 201-217, February.
    3. Neofytos Rodosthenous & Hongzhong Zhang, 2020. "When to sell an asset amid anxiety about drawdowns," Mathematical Finance, Wiley Blackwell, vol. 30(4), pages 1422-1460, October.
    4. Leippold, Markus & Vasiljević, Nikola, 2017. "Pricing and disentanglement of American puts in the hyper-exponential jump-diffusion model," Journal of Banking & Finance, Elsevier, vol. 77(C), pages 78-94.
    5. Zbigniew Palmowski & Jos'e Luis P'erez & Kazutoshi Yamazaki, 2020. "Double continuation regions for American options under Poisson exercise opportunities," Papers 2004.03330, arXiv.org.
    6. Huillet, Thierry & Möhle, Martin, 2013. "On the extended Moran model and its relation to coalescents with multiple collisions," Theoretical Population Biology, Elsevier, vol. 87(C), pages 5-14.
    7. Ghorbel, M. & Huillet, T., 2005. "Fragment size distributions in random fragmentations with cutoff," Statistics & Probability Letters, Elsevier, vol. 71(1), pages 47-60, January.
    8. Magdziarz, Marcin, 2009. "Stochastic representation of subdiffusion processes with time-dependent drift," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3238-3252, October.
    9. Long, Mingsi & Zhang, Hongzhong, 2019. "On the optimality of threshold type strategies in single and recursive optimal stopping under Lévy models," Stochastic Processes and their Applications, Elsevier, vol. 129(8), pages 2821-2849.
    10. Weissman, Ishay, 2023. "Some comments on “The density flatness phenomenon” by Alhakim and Molchanov and the Dickman distribution," Statistics & Probability Letters, Elsevier, vol. 194(C).
    11. Erhan Bayraktar, 2009. "On the perpetual American put options for level dependent volatility models with jumps," Quantitative Finance, Taylor & Francis Journals, vol. 11(3), pages 335-341.
    12. Meerschaert, Mark M. & Nane, Erkan & Xiao, Yimin, 2013. "Fractal dimension results for continuous time random walks," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1083-1093.
    13. Esmaeili, Habib & Klüppelberg, Claudia, 2010. "Parameter estimation of a bivariate compound Poisson process," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 224-233, October.
    14. Kwaśnicki, Mateusz & Małecki, Jacek & Ryznar, Michał, 2013. "First passage times for subordinate Brownian motions," Stochastic Processes and their Applications, Elsevier, vol. 123(5), pages 1820-1850.
    15. Jukka Lempa, 2008. "On infinite horizon optimal stopping of general random walk," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 67(2), pages 257-268, April.
    16. Çağlar, M. & Kyprianou, A. & Vardar-Acar, C., 2022. "An optimal stopping problem for spectrally negative Markov additive processes," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 1109-1138.
    17. Tine Compernolle & Kuno J. M. Huisman & Peter M. Kort & Maria Lavrutich & Cláudia Nunes & Jacco J. J. Thijssen, 2021. "Investment Decisions with Two-Factor Uncertainty," JRFM, MDPI, vol. 14(11), pages 1-17, November.
    18. 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.
    19. Dai, Darong & Shen, Kunrong, 2012. "A new stationary game equilibrium induced by stochastic group evolution and rational Individual choice," MPRA Paper 40133, University Library of Munich, Germany.
    20. Tim Siu-Tang Leung & Kazutoshi Yamazaki, 2010. "American Step-Up and Step-Down Default Swaps under Levy Models," Papers 1012.3234, arXiv.org, revised Sep 2012.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:126:y:2016:i:4:p:1124-1144. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.