# Pandemic-type failures in multivariate Brownian risk models

@article{Dbicki2022PandemictypeFI, title={Pandemic-type failures in multivariate Brownian risk models}, author={Krzysztof Dȩbicki and Enkelejd Hashorva and Nikolai Kriukov}, journal={Extremes}, year={2022}, volume={25}, pages={1 - 23} }

Modelling of multiple simultaneous failures in insurance, finance and other areas of applied probability is important especially from the point of view of pandemic-type events. A benchmark limiting model for the analysis of multiple failures is the classical d -dimensional Brownian risk model (Brm), see Delsing et al. (Methodol. Comput. Appl. Probab. 22 (3), 927–948 2020 ). From both theoretical and practical point of view, of interest is the calculation of the probability of multiple…

## 3 Citations

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

- MathematicsStatistics & Probability Letters
- 2022

### Extrema of multi-dimensional Gaussian processes over random intervals

- MathematicsJournal of Applied Probability
- 2022

The structure of the asymptotics of P(u) is determined by the signs of the drifts $c_i$'s, a relevant multi-dimensional regenerative model and the corresponding ruin probability are derived.

### Simultaneous ruin probability for multivariate gaussian risk model

- Mathematics
- 2021

Let Z(t) = (Z1(t), . . . , Zd(t)) ⊤, t ∈ R where Zi(t), t ∈ R, i = 1, ..., d are mutually independent centered Gaussian processes with continuous sample paths a.s. and stationary increments. For X(t)…

## References

SHOWING 1-10 OF 26 REFERENCES

### 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…

### 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…

### Exit problem of a two-dimensional risk process from the quadrant: Exact and asymptotic results.

- Mathematics
- 2008

Consider two insurance companies (or two branches of the same company) that divide between them both claims and premia in some specified proportions. We model the occurrence of claims according to a…

### Asymptotics and Approximations of Ruin Probabilities for Multivariate Risk Processes in a Markovian Environment

- MathematicsMethodology and Computing in Applied Probability
- 2019

This paper develops asymptotics and approximations for ruin probabilities in a multivariate risk setting. We consider a model in which the individual reserve processes are driven by a common…

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

- MathematicsStochastic Processes and their Applications
- 2018

### The exact asymptotics of the large deviation probabilities in the multivariate boundary crossing problem

- MathematicsAdvances in Applied Probability
- 2019

Abstract For a multivariate random walk with independent and identically distributed jumps satisfying the Cramér moment condition and having mean vector with at least one negative component, we…

### The Exact Asymptotics for Hitting Probability of a Remote Orthant by a Multivariate Lévy Process: The Cramér Case

- Mathematics2017 MATRIX Annals
- 2019

For a multivariate Levy process satisfying the Cramer moment condition and having a drift vector with at least one negative component, we derive the exact asymptotics of the probability of ever…

### High order expansions for renewal functions and applications to ruin theory

- Mathematics
- 2017

A high order expansion of the renewal function is provided under the assumption that the inter-renewal time distribution is light tailed with finite moment generating function g on a neighborhood of…

### 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…