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Estimation of the parameters of a Markov-modulated loss process in insurance

Author

Listed:
  • Armelle Guillou

    (IRMA - Institut de Recherche Mathématique Avancée - UNISTRA - Université de Strasbourg - CNRS - Centre National de la Recherche Scientifique)

  • Stéphane Loisel

    (SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

  • Gilles Stupfler

    (IRMA - Institut de Recherche Mathématique Avancée - UNISTRA - Université de Strasbourg - CNRS - Centre National de la Recherche Scientifique)

Abstract

We present a new model of loss processes in insurance. The process is a couple $(N, \, L)$ where $N$ is a univariate Markov-modulated Poisson process (MMPP) and $L$ is a multivariate loss process whose behaviour is driven by $N$. We prove the strong consistency of the maximum likelihood estimator of the parameters of this model, and present an EM algorithm to compute it in practice. The method is illustrated with simulations and real sets of insurance data.

Suggested Citation

  • Armelle Guillou & Stéphane Loisel & Gilles Stupfler, 2013. "Estimation of the parameters of a Markov-modulated loss process in insurance," Post-Print hal-00589696, HAL.
    • Handle: RePEc:hal:journl:hal-00589696
    DOI: 10.1016/j.insmatheco.2013.07.003
    Note: View the original document on HAL open archive server: https://hal.science/hal-00589696
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    Cited by:

    1. Lesław Gajek & Marcin Rudź, 2020. "Finite-Horizon Ruin Probabilities in a Risk-Switching Sparre Andersen Model," Methodology and Computing in Applied Probability, Springer, vol. 22(4), pages 1493-1506, December.
    2. F. Baltazar-Larios & Luz Judith R. Esparza, 2022. "Statistical Inference for Partially Observed Markov-Modulated Diffusion Risk Model," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 571-593, June.
    3. Gajek, Lesław & Rudź, Marcin, 2018. "Banach Contraction Principle and ruin probabilities in regime-switching models," Insurance: Mathematics and Economics, Elsevier, vol. 80(C), pages 45-53.
    4. Avanzi, Benjamin & Taylor, Greg & Wong, Bernard & Xian, Alan, 2021. "Modelling and understanding count processes through a Markov-modulated non-homogeneous Poisson process framework," European Journal of Operational Research, Elsevier, vol. 290(1), pages 177-195.
    5. Lesław Gajek & Marcin Rudź, 2020. "Finite-horizon general insolvency risk measures in a regime-switching Sparre Andersen model," Methodology and Computing in Applied Probability, Springer, vol. 22(4), pages 1507-1528, December.
    6. Gajek, Lesław & Rudź, Marcin, 2017. "A generalization of Gerber’s inequality for ruin probabilities in risk-switching models," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 236-240.

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