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First Passage Time of Filtered Poisson Process with Exponential Shape Function

Author

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

Abstract

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
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    File URL: http://www.qfrc.uts.edu.au/research/research_papers/rp109.pdf
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    References listed on IDEAS

    as
    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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    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, arXiv.org.
    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

    Keywords

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

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