# 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} }

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 probability for two-dimensional Brownian risk model

- MathematicsStatistics & Probability Letters
- 2021

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

- Mathematics
- 2022

: 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…

### Uniform bounds for ruin probability in multidimensional risk model

- MathematicsStatistics & Probability Letters
- 2022

### Sojourn Ruin of a Two-Dimensional Fractional Brownian Motion Risk Process

- Mathematics
- 2021

This paper derives the asymptotic behavior of

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