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

By Angelos Dassios and Jiwook Jang


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

Topics: HA Statistics
Publisher: Hindawi Publishing Corporation
Year: 2008
DOI identifier: 10.1155/2008
OAI identifier:
Provided by: LSE Research Online

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  1. (1979). An Introduction to Mathematical Risk Theory, doi
  2. Arbitrage-free premium calculation for extreme losses using the shot noise process and the Esscher transform,” doi
  3. (1991). Aspects of Risk Theory, Springer Series in Statistics: Probability and Its Applications, doi
  4. (1972). Conditional Poisson processes,” doi
  5. (1998). Doubly stochastic point processes in reinsurance and the pricing of catastrophe insurance derivatives, Ph. D Thesis, The London School of Economics and Political Science,
  6. (1995). Explosive Poisson shot noise processes with applications to risk reserves,” doi
  7. (2002). Generalized Poisson Models and Their Applications in Insurance and Finance, doi
  8. (1975). inlar ,Introduction to Stochastic Processes,
  9. (1987). Insurance, storage and point process: an approach via piecewise deterministic Markov processes, Ph. D Thesis,
  10. (2007). Jump diffusion processes and their applications in insurance and finance,” doi
  11. (2004). Martingale approach for moments of discounted aggregate claims,” doi
  12. (1989). Martingales and insurance risk,” doi
  13. (1930). On the Mathematical Theory of Risk, Skandia Jubilee Volume,
  14. (1984). Piecewise-deterministic Markov processes: a general class of nondiffusion stochastic models,”
  15. (1981). Point Processes and Queues. Martingale Dynamics, doi
  16. (2003). Pricing of catastrophe reinsurance and derivatives using the Cox process with shot noise intensity,” doi
  17. (1984). Risk Theory. The Stochastic Basis of Insurance,
  18. (1955). Some statistical methods connected with series of events,”
  19. (1999). Stochastic Processes for Insurance and Finance, doi
  20. (1982). Stochastic Processes, doi
  21. The Poisson process: its failure in risk theory,” doi
  22. (1963). The spectral analysis of point processes,” doi
  23. (1966). The Statistical Analysis of Series of Events, doi
  24. (1986). The virtual waiting-time and related processes,” doi
  25. uhlmann, Mathematical Methods in Risk Theory, Die Grundlehren der Mathematischen Wissenschaften, doi

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