# Parisian Ruin for Insurer and Reinsurer under Quata-Share Treaty

@inproceedings{Jasnovidov2021ParisianRF, title={Parisian Ruin for Insurer and Reinsurer under Quata-Share Treaty}, author={Grigori Jasnovidov and Aleksandr A. Shemendyuk}, year={2021} }

In this contribution we study asymptotics of the simultaneous Parisian ruin probability of a two-dimensional fractional Brownian motion risk process. This risk process models the surplus processes of an insurance and a reinsurance companies, where the net loss is distributed between them in given proportions. We also propose an approach for simulation of Pickands and Piterbarg constants appearing in the asymptotics of the ruin probability. AMS Classification: Primary 60G15; secondary 60G70

## 3 Citations

### On the speed of convergence of Piterbarg constants

- Mathematics
- 2022

: In this paper we derive an upper bound for the diﬀerence between the continuous and discrete Piterbarg constants. Our result allows us to approximate the classical Piterbarg constants by their…

### On the speed of convergence of discrete Pickands constants to continuous ones

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- 2021

In this manuscript, we address open questions raised by Dieker & Yakir (2014), who proposed a novel method of estimation of (discrete) Pickands constants Hδ α using a family of estimators ξδ α(T ), T…

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

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- 2021

This paper derives the asymptotic behavior of

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