Weak limits of random coefficient autoregressive processes and their application in ruin theory

Y. Dong and J. Spielmann

Insurance: Mathematics and Economics, 2020, vol. 91, issue C, 1-11

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; Weak convergence; Autoregressive process; Stochastic recurrence equation; Generalized Ornstein–Uhlenbeck process; Ruin probability; First passage time (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:91:y:2020:i:c:p:1-11

DOI: 10.1016/j.insmatheco.2019.12.001

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