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Risk models based on time series for count random variables


  • Cossette, Hélène
  • Marceau, Étienne
  • Toureille, Florent


In this paper, we generalize the classical discrete time risk model by introducing a dependence relationship in time between the claim frequencies. The models used are the Poisson autoregressive model and the Poisson moving average model. In particular, the aggregate claim amount and related quantities such as the stop-loss premium, value at risk and tail value at risk are discussed within this framework.

Suggested Citation

  • Cossette, Hélène & Marceau, Étienne & Toureille, Florent, 2011. "Risk models based on time series for count random variables," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 19-28, January.
  • Handle: RePEc:eee:insuma:v:48:y:2011:i:1:p:19-28

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    References listed on IDEAS

    1. Promislow, S. David, 1991. "The probability of ruin in a process with dependent increments," Insurance: Mathematics and Economics, Elsevier, vol. 10(2), pages 99-107, July.
    2. Gerber, Hans U., 1982. "Ruin theory in the linear model," Insurance: Mathematics and Economics, Elsevier, vol. 1(3), pages 213-217, July.
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    Cited by:

    1. Zhao, Xiaobing & Zhou, Xian, 2012. "Copula models for insurance claim numbers with excess zeros and time-dependence," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 191-199.


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