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

Yuchao Dong; Jérôme Spielmann

doi:10.1016/j.insmatheco.2019.12.001

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arXiv · 1907.01828

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

Yuchao Dong·Jérôme Spielmann

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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.

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Yuchao Dong, Jérôme Spielmann. 2019-07-03. Weak Limits of Random Coefficient Autoregressive Processes and their Application in Ruin Theory. https://doi.org/10.1016/j.insmatheco.2019.12.001

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