# On the cumulative Parisian ruin of multi-dimensional Brownian motion risk models

@article{Ji2020OnTC,
title={On the cumulative Parisian ruin of multi-dimensional Brownian motion risk models},
author={Lanpeng Ji},
journal={Scandinavian Actuarial Journal},
year={2020},
volume={2020},
pages={819 - 842}
}
• L. Ji
• Published 26 November 2018
• Mathematics
• Scandinavian Actuarial Journal
Consider a multi-dimensional Brownian motion which models the surplus processes of multiple lines of business of an insurance company. Our main result gives exact asymptotics for the cumulative Parisian ruin probability as the initial capital tends to infinity. An asymptotic distribution for the conditional cumulative Parisian ruin time is also derived. The obtained results on the cumulative Parisian ruin can be seen as generalisations of some of the results derived in D bicki et al. [(2018…
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