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The distribution of the interval between events of a Cox process with shot noise intensity

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  • Dassios, Angelos
  • Jang, Jiwook

Abstract

Applying piecewise deterministic Markov processes theory, the probability generating function of a Cox process, incorporating with shot noise process as the claim intensity, is obtained. We also derive the Laplace transform of the distribution of the shot noise process at claim jump times, using stationary assumption of the shot noise process at any times. Based on this Laplace transform and from the probability generating function of a Cox process with shot noise intensity, we obtain the distribution of the interval of a Cox process with shot noise intensity for insurance claims and its moments, that is, mean and variance.

Suggested Citation

  • Dassios, Angelos & Jang, Jiwook, 2008. "The distribution of the interval between events of a Cox process with shot noise intensity," LSE Research Online Documents on Economics 31864, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:31864
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    File URL: http://eprints.lse.ac.uk/31864/
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    Cited by:

    1. Alan Genaro & Adilson Simonis, 2015. "Estimating doubly stochastic Poisson process with affine intensities by Kalman filter," Statistical Papers, Springer, vol. 56(3), pages 723-748, August.
    2. Alan De Genaro Dario & Adilson Simonis, 2011. "Properties of Doubly Stochastic Poisson Process with affine intensity," Papers 1109.2884, arXiv.org, revised Sep 2011.
    3. Ghislain Léveillé & Emmanuel Hamel, 2018. "Conditional, Non-Homogeneous and Doubly Stochastic Compound Poisson Processes with Stochastic Discounted Claims," Methodology and Computing in Applied Probability, Springer, vol. 20(1), pages 353-368, March.

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    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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