IDEAS home Printed from https://ideas.repec.org/p/ehl/lserod/3219.html
   My bibliography  Save this paper

The disorder problem for compound Poisson processes with exponential jumps

Author

Listed:
  • Gapeev, Pavel V.

Abstract

The problem of disorder seeks to determine a stopping time which is as close as possible to the unknown time of “disorder” when the observed process changes its probability characteristics. We give a partial answer to this question for some special cases of Lévy processes and present a complete solution of the Bayesian and variational problem for a compound Poisson process with exponential jumps. The method of proof is based on reducing the Bayesian problem to an integro-differential free-boundary problem where, in some cases, the smooth-fit principle breaks down and is replaced by the principle of continuous fit.

Suggested Citation

  • Gapeev, Pavel V., 2005. "The disorder problem for compound Poisson processes with exponential jumps," LSE Research Online Documents on Economics 3219, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:3219
    as

    Download full text from publisher

    File URL: http://eprints.lse.ac.uk/3219/
    File Function: Open access version.
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ernesto Mordecki, 1999. "Optimal stopping for a diffusion with jumps," Finance and Stochastics, Springer, vol. 3(2), pages 227-236.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Asaf Cohen, 2015. "Parameter Estimation: The Proper Way to Use Bayesian Posterior Processes with Brownian Noise," Mathematics of Operations Research, INFORMS, vol. 40(2), pages 361-389, February.
    2. Asaf Cohen & Eilon Solan, 2013. "Bandit Problems with Lévy Processes," Mathematics of Operations Research, INFORMS, vol. 38(1), pages 92-107, February.
    3. Erhan Bayraktar & H. Poor, 2008. "Optimal time to change premiums," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 68(1), pages 125-158, August.
    4. Gapeev, Pavel V., 2006. "Multiple disorder problems for Wiener and compound Poisson processes with exponential jumps," SFB 649 Discussion Papers 2006-074, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    5. Savas Dayanik & Semih O Sezer, 2023. "Model Misspecification in Discrete Time Bayesian Online Change Detection," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-27, March.
    6. repec:hum:wpaper:sfb649dp2006-074 is not listed on IDEAS
    7. Krawiec, Michał & Palmowski, Zbigniew & Płociniczak, Łukasz, 2018. "Quickest drift change detection in Lévy-type force of mortality model," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 432-450.
    8. Bruno Buonaguidi, 2023. "Finite Horizon Sequential Detection with Exponential Penalty for the Delay," Journal of Optimization Theory and Applications, Springer, vol. 198(1), pages 224-238, July.
    9. Gapeev, Pavel V., 2006. "Integral options in models with jumps," SFB 649 Discussion Papers 2006-068, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    10. Savas Dayanik & Semih Onur Sezer, 2006. "Compound Poisson Disorder Problem," Mathematics of Operations Research, INFORMS, vol. 31(4), pages 649-672, November.
    11. Gapeev, Pavel V. & Stoev, Yavor I., 2017. "On the Laplace transforms of the first exit times in one-dimensional non-affine jump–diffusion models," Statistics & Probability Letters, Elsevier, vol. 121(C), pages 152-162.
    12. repec:hum:wpaper:sfb649dp2006-068 is not listed on IDEAS
    13. Gapeev, Pavel V. & Jeanblanc, Monique, 2024. "On the construction of conditional probability densities in the Brownian and compound Poisson filtrations," LSE Research Online Documents on Economics 121059, London School of Economics and Political Science, LSE Library.

    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. Gapeev, Pavel V., 2006. "On maximal inequalities for some jump processes," SFB 649 Discussion Papers 2006-060, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    2. S. G. Kou & Hui Wang, 2004. "Option Pricing Under a Double Exponential Jump Diffusion Model," Management Science, INFORMS, vol. 50(9), pages 1178-1192, September.
    3. Marc Chesney & Laurent Gauthier, 2006. "American Parisian options," Finance and Stochastics, Springer, vol. 10(4), pages 475-506, December.
    4. Barrieu, Pauline & Bellamy, N., 2007. "Optimal hitting time and perpetual option in a non-Lévy model: application to real options," LSE Research Online Documents on Economics 5099, London School of Economics and Political Science, LSE Library.
    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.
    6. Décamps, Jean-Paul & Mariotti, Thomas & Villeneuve, Stéphane, 2000. "Investment Timing under Incomplete Information," IDEI Working Papers 115, Institut d'Économie Industrielle (IDEI), Toulouse, revised Apr 2004.
    7. Kleinert, Florian & van Schaik, Kees, 2015. "A variation of the Canadisation algorithm for the pricing of American options driven by Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 125(8), pages 3234-3254.
    8. Gapeev, Pavel V., 2006. "Integral options in models with jumps," SFB 649 Discussion Papers 2006-068, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    9. Jean-Paul Décamps & Thomas Mariotti & Stéphane Villeneuve, 2005. "Investment Timing Under Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 30(2), pages 472-500, May.
    10. Gapeev Pavel V. & Kühn Christoph, 2005. "Perpetual convertible bonds in jump-diffusion models," Statistics & Risk Modeling, De Gruyter, vol. 23(1/2005), pages 15-31, January.
    11. repec:hum:wpaper:sfb649dp2006-060 is not listed on IDEAS
    12. Ming-Chi Chang & Yuan-Chung Sheu, 2013. "Free boundary problems and perpetual American strangles," Quantitative Finance, Taylor & Francis Journals, vol. 13(8), pages 1149-1155, July.
    13. Gapeev, Pavel V., 2008. "The integral option in a model with jumps," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2623-2631, November.
    14. Gapeev, Pavel V., 2006. "Discounted optimal stopping for maxima of some jump-diffusion processes," SFB 649 Discussion Papers 2006-059, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    15. Christian Flor & Simon Hansen, 2013. "Technological advances and the decision to invest," Annals of Finance, Springer, vol. 9(3), pages 383-420, August.
    16. Gapeev, Pavel V. & Stoev, Yavor I., 2017. "On the Laplace transforms of the first exit times in one-dimensional non-affine jump–diffusion models," Statistics & Probability Letters, Elsevier, vol. 121(C), pages 152-162.
    17. repec:hum:wpaper:sfb649dp2006-068 is not listed on IDEAS
    18. Gapeev Pavel V. & Rodosthenous Neofytos, 2013. "Perpetual American options in a diffusion model with piecewise-linear coefficients," Statistics & Risk Modeling, De Gruyter, vol. 30(1), pages 1-21, March.
    19. Philipp N. Baecker, 2007. "Real Options and Intellectual Property," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-48264-2, October.

    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:ehl:lserod:3219. 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: LSERO Manager (email available below). General contact details of provider: https://edirc.repec.org/data/lsepsuk.html .

    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.