IDEAS home Printed from
   My bibliography  Save this paper

First Passage Time of Filtered Poisson Process with Exponential Shape Function


  • Alexander Novikov
  • R. E. Melchers
  • E. Shinjikashvili
  • N. Kordzakhia


Solving some integro-differential equation we find the Laplace transformation of the first passage time for Filtered Poisson Process generated by pulses with uniform or exponential distributions. Also, the martingale technique is applied for approximations of expectations accuracy is veryfying with the help of Monte-Carlo simulations.

Suggested Citation

  • Alexander Novikov & R. E. Melchers & E. Shinjikashvili & N. Kordzakhia, 2003. "First Passage Time of Filtered Poisson Process with Exponential Shape Function," Research Paper Series 109, Quantitative Finance Research Centre, University of Technology, Sydney.
  • Handle: RePEc:uts:rpaper:109

    Download full text from publisher

    File URL:
    Download Restriction: no

    References listed on IDEAS

    1. Tsurui, Akira & Osaki, Shunji, 1976. "On a first-passage problem for a cumulative process with exponential decay," Stochastic Processes and their Applications, Elsevier, vol. 4(1), pages 79-88, January.
    2. Olivier Scaillet & Boris Leblanc, 1998. "Path dependent options on yields in the affine term structure model," Finance and Stochastics, Springer, vol. 2(4), pages 349-367.
    Full references (including those not matched with items on IDEAS)


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

    Cited by:

    1. Jacobsen, Martin & Jensen, Anders Tolver, 2007. "Exit times for a class of piecewise exponential Markov processes with two-sided jumps," Stochastic Processes and their Applications, Elsevier, vol. 117(9), pages 1330-1356, September.
    2. Borovkov, Konstantin & Novikov, Alexander, 2008. "On exit times of Lévy-driven Ornstein-Uhlenbeck processes," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1517-1525, September.
    3. Habtemicael, Semere & SenGupta, Indranil, 2014. "Ornstein–Uhlenbeck processes for geophysical data analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 399(C), pages 147-156.
    4. Soeren Asmussen & Dilip Madan & Martijn Pistorius, 2007. "Pricing Equity Default Swaps under an approximation to the CGMY L\'{e}% vy Model," Papers 0711.2807,
    5. Zhou, Jiang & Wu, Lan & Bai, Yang, 2017. "Occupation times of Lévy-driven Ornstein–Uhlenbeck processes with two-sided exponential jumps and applications," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 80-90.

    More about this item


    first passage times; laplace transformation; martingales; integro-differential equations; filtered poisson process; ornstein-uhlenbeck process;

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    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:uts:rpaper:109. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Duncan Ford). General contact details of provider: .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.