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A claims persistence process and insurance

Author

Listed:
  • Vallois, Pierre
  • Tapiero, Charles S.

Abstract

The purpose of this paper is to introduce and construct a state dependent counting and persistent random walk. Persistence is imbedded in a Markov chain for predicting insured claims based on their current and past period claim. We calculate for such a process, the probability generating function of the number of claims over time and as a result are able to calculate their moments. Further, given the claims severity probability distribution, we provide both the claims process generating function as well as the mean and the claim variance that an insurance firm confronts over a given period of time and in such circumstances. A number of results and applictions are then outlined (such as a Compound Claim Persistence Process).

Suggested Citation

  • Vallois, Pierre & Tapiero, Charles S., 2009. "A claims persistence process and insurance," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 367-373, June.
    • Handle: RePEc:eee:insuma:v:44:y:2009:i:3:p:367-373
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    References listed on IDEAS

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    1. Vallois, Pierre & Tapiero, Charles S., 2007. "Memory-based persistence in a counting random walk process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 386(1), pages 303-317.
    2. Weiss, George H, 2002. "Some applications of persistent random walks and the telegrapher's equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 311(3), pages 381-410.
    3. Pottier, Noëlle, 1996. "Analytic study of the effect of persistence on a one-dimensional biased random walk," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 230(3), pages 563-576.
    4. Telesca, Luciano & Lovallo, Michele, 2006. "Are global terrorist attacks time-correlated?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 362(2), pages 480-484.
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    Cited by:

    1. Ramírez-Cobo, Pepa & Carrizosa, Emilio & Lillo, Rosa E., 2021. "Analysis of an aggregate loss model in a Markov renewal regime," Applied Mathematics and Computation, Elsevier, vol. 396(C).

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