# Parisian & cumulative Parisian ruin probability for two-dimensional Brownian risk model

@article{Kriukov2021ParisianC,
title={Parisian \& cumulative Parisian ruin probability for two-dimensional Brownian risk model},
author={Nikolai Kriukov},
journal={Stochastics},
year={2021},
volume={94},
pages={629 - 645}
}
• N. Kriukov
• Published 25 January 2020
• Mathematics
• Stochastics
Parisian ruin probability in the classical Brownian risk model, unlike the standard ruin probability can not be explicitly calculated even in one-dimensional setup. Resorting on asymptotic theory, we derive in this contribution the asymptotic approximations of both Parisian and cumulative Parisian ruin probabilities and simultaneous ruin time for the two-dimensional Brownian risk model when the initial capital increases to infinity.
4 Citations

### Parisian ruin with power-asymmetric variance near the optimal point with application to many-inputs proportional reinsurance

: This paper investigates the Parisian ruin probability for processes with power-asymmetric behavior of the variance near the unique optimal point. We derive the exact asymptotics as the ruin

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