• Corpus ID: 232110661

# 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}
}
• Published 4 March 2021
• Mathematics
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

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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

## References

SHOWING 1-10 OF 30 REFERENCES

### Ruin problem of a two-dimensional fractional Brownian motion risk process

• Mathematics
• 2018
ABSTRACT This paper investigates ruin probability and ruin time of a two-dimensional fractional Brownian motion risk process. The net loss process of an insurance company is modeled by a fractional

### Parisian ruin over a finite-time horizon

• Mathematics
• 2016
For a risk process Ru(t) = u + ct − X(t), t ≥ 0, where u ≥ 0 is the initial capital, c > 0 is the premium rate and X(t), t ≥ 0 is an aggregate claim process, we investigate the probability of the

### On asymptotic constants in the theory of extremes for Gaussian processes

• Computer Science, Mathematics
• 2012
This paper gives a new representation of Pickands' constants, which arise in the study of extremes for a variety of Gaussian processes, and resolves the long-standing problem of devising a reliable algorithm for estimating these constants.

### Parisian ruin of self-similar Gaussian risk processes

• Mathematics
Journal of Applied Probability
• 2015
The exact asymptotics of the probability of Parisian ruin for self-similar Gaussian risk processes are derived and an asymPTotic relation between the Parisian and the classical ruin times is derived.

### EXTREMES OF γ-REFLECTED GAUSSIAN PROCESSES WITH STATIONARY INCREMENTS

• Mathematics
• 2018
For a given centered Gaussian process with stationary increments X(t), t ≥ 0 and c > 0, let Wγ(t) = X(t)− ct− γ inf 0≤s≤t (X(s)− cs) , t ≥ 0 denote the γ-reflected process, where γ ∈ (0, 1). This

### High Excursions of Gaussian Nonstationary Processes in Discrete Time

• Mathematics
• 2021
Exact asymptotic behavior is given for high excursion probabilities of Gaussian processes in discrete time as the corresponding lattice pitch unboundedly decreases. The proximity of the asymptotic

### Simultaneous Ruin Probability for Two-Dimensional Fractional Brownian Motion Risk Process over Discrete Grid

This paper derives the asymptotic behavior of the following ruin probability $$P\{\exists t \in G(\delta):B_H(t)-c_1t>q_1u,B_H(t)-c_2t>q_2u\}, \ \ \ u \rightarrow \infty,$$ where $B_H$ is a standard

### Approximation of ruin probability and ruin time in discrete Brownian risk models

We analyze the classical Brownian risk models discussing the approximation of ruin probabilities (classical, γ-reflected, Parisian and cumulative Parisian) for the case that ruin can occur only on