First Passage Time of Filtered Poisson Process with Exponential Shape Function
AbstractSolving 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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Bibliographic InfoPaper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 109.
Date of creation: 01 Oct 2003
Date of revision:
first passage times; laplace transformation; martingales; integro-differential equations; filtered poisson process; ornstein-uhlenbeck process;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2004-06-02 (All new papers)
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- 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.
- 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.
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