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Risk models based on time series for count random variables

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

Abstract

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

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    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. Gordon Willmot & Jae-Kyung Woo, 2007. "On the Class of Erlang Mixtures with Risk Theoretic Applications," North American Actuarial Journal, Taylor & Francis Journals, vol. 11(2), pages 99-115.
    3. 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. Boris Aleksandrov & Christian H. Weiß, 2020. "Parameter estimation and diagnostic tests for INMA(1) processes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 196-232, March.
    2. Xiang Hu & Lianzeng Zhang, 2016. "Ruin Probability in a Correlated Aggregate Claims Model with Common Poisson Shocks: Application to Reinsurance," Methodology and Computing in Applied Probability, Springer, vol. 18(3), pages 675-689, September.
    3. 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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