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Memory-based persistence in a counting random walk process

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  • Vallois, Pierre
  • Tapiero, Charles S.
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    Abstract

    This paper considers a memory-based persistent counting random walk, based on a Markov memory of the last event. This persistent model is a different than the Weiss persistent random walk model however, leading thereby to different results. We point out to some preliminary result, in particular, we provide an explicit expression for the mean and the variance, both nonlinear in time, of the underlying memory-based persistent process and discuss the usefulness to some problems in insurance, finance and risk analysis. The motivation for the paper arose from the counting of events (whether rare or not) in insurance that presume that events are time independent and therefore based on the Poisson distribution for counting these events.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0378437107008758
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    Bibliographic Info

    Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

    Volume (Year): 386 (2007)
    Issue (Month): 1 ()
    Pages: 303-317

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    Handle: RePEc:eee:phsmap:v:386:y:2007:i:1:p:303-317

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    Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/

    Related research

    Keywords: Persistence; Random walk; Insurance; Markov chains;

    References

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    1. Masoliver, Jaume & Montero, Miquel & Perelló, Josep & Weiss, George H., 2007. "The CTRW in finance: Direct and inverse problems with some generalizations and extensions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(1), pages 151-167.
    2. Scalas, Enrico, 2006. "The application of continuous-time random walks in finance and economics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 362(2), pages 225-239.
    3. 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.
    4. 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.
    5. Jaume Masoliver & Miquel Montero & George H. Weiss, 2002. "A continuous time random walk model for financial distributions," Papers cond-mat/0210513, arXiv.org.
    6. 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.
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    Cited by:
    1. Vallois, Pierre & Tapiero, Charles S., 2009. "A claims persistence process and insurance," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 367-373, June.

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