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

Yuchao Dong () and Jérôme Spielmann ()
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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

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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.

Keywords: Invariance principle; Autoregressive processes; Stochastic recurrence equations; weak convergence; autoregressive pro- cess; stochastic recurrence equation; generalized Ornstein-Uhlenbeck process; ruin probability; first passage time (search for similar items in EconPapers)
Date: 2020-03
Note: View the original document on HAL open archive server: https://hal.science/hal-02170829v2
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Published in Insurance: Mathematics and Economics, 2020, 91, pp.1-11. ⟨10.1016/j.insmatheco.2019.12.001⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-02170829

DOI: 10.1016/j.insmatheco.2019.12.001

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