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Weak Limits of Random Coefficient Autoregressive Processes and their Application in Ruin Theory

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  • Yuchao Dong

    (LASP - Laboratory for Atmospheric and Space Physics [Boulder] - University of Colorado [Boulder])

  • Jérôme Spielmann

    (LAREMA - Laboratoire Angevin de Recherche en Mathématiques - UA - Université d'Angers - CNRS - Centre National de la Recherche Scientifique, UA - Université d'Angers)

Abstract

We prove that a large class of discrete-time insurance surplus processes converge weakly to a generalized Ornstein-Uhlenbeck process, under a suitable re-normalization and when the time-step goes to 0. Motivated by ruin theory, we use this result to obtain approximations for the moments, the ultimate ruin probability and the discounted penalty function of the discrete-time process.

Suggested Citation

  • Yuchao Dong & Jérôme Spielmann, 2020. "Weak Limits of Random Coefficient Autoregressive Processes and their Application in Ruin Theory," Post-Print hal-02170829, HAL.
    • Handle: RePEc:hal:journl:hal-02170829
    DOI: 10.1016/j.insmatheco.2019.12.001
    Note: View the original document on HAL open archive server: https://hal.science/hal-02170829v2
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    References listed on IDEAS

    as
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