Weak Limits of Random Coefficient Autoregressive Processes and their Application in Ruin Theory
Probability
2020-07-16 v2 Risk Management
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.
Cite
@article{arxiv.1907.01828,
title = {Weak Limits of Random Coefficient Autoregressive Processes and their Application in Ruin Theory},
author = {Yuchao Dong and Jérôme Spielmann},
journal= {arXiv preprint arXiv:1907.01828},
year = {2020}
}