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

@article{Dbicki2018ExtremalBO, title={Extremal behavior of hitting a cone by correlated Brownian motion with drift}, author={Krzysztof Dȩbicki and Enkelejd Hashorva and Lanpeng Ji and Tomasz Rolski}, journal={Stochastic Processes and their Applications}, year={2018} }

## 18 Citations

### 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…

### Finite-time ruin probability for correlated Brownian motions

- MathematicsScandinavian Actuarial Journal
- 2020

Let be a two-dimensional Gaussian process with standard Brownian motion marginals and constant correlation . Define the joint survival probability of both supremum functionals by where and u, v are…

### 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…

### Tail asymptotics for Shepp-statistics of Brownian motion in ℝ d

- Mathematics
- 2020

Let $X(t)$, $t\in R$, be a $d$-dimensional vector-valued Brownian motion, $d\ge 1$. For all $b\in R^d\setminus (-\infty,0]^d$ we derive exact asymptotics of \[ P(X(t+s)-X(t) >u b\mbox{ for some…

### Logarithmic Asymptotics for Probability of Component-Wise Ruin in a Two-Dimensional Brownian Model

- MathematicsRisks
- 2019

We consider a two-dimensional ruin problem where the surplus process of business lines is modelled by a two-dimensional correlated Brownian motion with drift. We study the ruin function P ( u ) for…

### Extremes of vector-valued Gaussian processes

- MathematicsStochastic Processes and their Applications
- 2020

### Dominating Points of Gaussian Extremes

- Mathematics
- 2018

We quantify the large deviations of Gaussian extreme value statistics on closed convex sets in d-dimensional Euclidean space. The asymptotics imply that the extreme value distribution exhibits a rate…

### Simultaneous Ruin Probability for Two-Dimensional Brownian and L\'evy Risk Models

- Mathematics
- 2018

The ruin probability in the classical Brownian risk model can be explicitly calculated for both finite and infinite-time horizon. This is not the case for the simultaneous ruin probability in…

### Pandemic-type failures in multivariate Brownian risk models

- MathematicsExtremes
- 2022

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…

### Exact asymptotics of component-wise extrema of two-dimensional Brownian motion

- Mathematics
- 2020

We derive the exact asymptotics of \[ P\left( \sup_{t\ge 0} \Bigl( X_1(t) - \mu_1 t\Bigr)> u, \ \sup_{s\ge 0} \Bigl( X_2(s) - \mu_2 s\Bigr)> u \right), \ \ u\to\infty, \] where…

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