First Passage Time of Filtered Poisson Process with Exponential Shape Function
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.
|Date of creation:||01 Oct 2003|
|Date of revision:|
|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.|
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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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