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

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.
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https://hal.archives-ouvertes.fr/hal-02170829
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Submitted on : Thursday, February 13, 2020 - 4:46:05 PM
Last modification on : Wednesday, November 3, 2021 - 9:18:32 AM

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Yuchao Dong, Jérôme Spielmann. Weak Limits of Random Coefficient Autoregressive Processes and their Application in Ruin Theory. Insurance: Mathematics and Economics, Elsevier, 2020, 91, pp.1-11. ⟨10.1016/j.insmatheco.2019.12.001⟩. ⟨hal-02170829v2⟩

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