## References

SHOWING 1-10 OF 29 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 & cumulative Parisian ruin probability for two-dimensional Brownian risk model

- MathematicsStochastics
- 2021

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…

Parisian ruin of self-similar Gaussian risk processes

- MathematicsJournal 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.

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

- MathematicsScandinavian Actuarial Journal
- 2020

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…

Asymptotics of Parisian ruin of Brownian motion risk model over an infinite-time horizon

- Mathematics
- 2017

Abstract Let be a standard Brownian motion. In this paper, we derive the asymptotics of the probability of Parisian ruin over an infinite time horizon for the following risk process (0.1) where is…

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…

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

- Mathematics
- 2020

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…

Parisian Ruin for Insurer and Reinsurer under Quata-Share Treaty

- Mathematics
- 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…

Extremal behavior of hitting a cone by correlated Brownian motion with drift

- MathematicsStochastic Processes and their Applications
- 2018

Asymptotic Methods in the Theory of Gaussian Processes and Fields

- Mathematics
- 1995

Introduction The method of comparison The double sum method The method of moments Limit theorems for the number of high excursions and for maxima of Gaussian processes and fields References.