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First Passage Time of Filtered Poisson Process with Exponential Shape Function

Listed author(s):
  • Alexander Novikov
  • R. E. Melchers
  • E. Shinjikashvili
  • N. Kordzakhia
Registered author(s):

    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.

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    Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 109.

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    Length: 19 pages
    Date of creation: 01 Oct 2003
    Publication status: Published as: Novikov, A., Melchers, R. E., Shinjikashvili, E. and Kordzakhia, N., 2006, "First Passage Time of Filtered Poisson Process with Exponential Shape Function", Probabilistic Engineering Mechanics, 20(1), 57-66.
    Handle: RePEc:uts:rpaper:109
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    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.
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