5 citations · 8 across the 6 of their papers we have counts for
11 papers
Finite-time ruin probability for correlated Brownian motions
Krzysztof Dȩbicki, Enkelejd Hashorva, Konrad Krystecki
Let be a bivariate Brownian motion with standard Brownian motion marginals and constant correlation and define the joint survival probabi…
Exact asymptotics of component-wise extrema of two-dimensional Brownian motion
Krzysztof Debicki, Lanpeng Ji, Tomasz Rolski
We derive the exact asymptotics of \[ P\left( \sup_{t\ge 0} \Bigl( X_1(t) - μ_1 t\Bigr)> u, \ \sup_{s\ge 0} \Bigl( X_2(s) - μ_2 s\Bigr)> u \right), \ \ u\to\infty, \] where $(X_1(t…
Logarithmic asymptotics for probability of component-wise ruin in a two-dimensional Brownian model
Krzysztof Debicki, Lanpeng Ji, Tomasz Rolski
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 fun…
Pickands-Piterbarg constants for self-similar Gaussian processes
Krzysztof Dȩbicki, Kamil Tabiś
For a centered self-similar Gaussian process and we analyze asymptotic behaviour of \[ \mathcal{H}_Y^R(T) \; = \; \mathbf{E} \exp \left( \sup_{t \…
The time of ultimate recovery in Gaussian risk model
Krzysztof Debicki, Peng Liu
We analyze the distance between the first and the last passage time of at level in time horizon , where is a cen…
Extremes of vector-valued Gaussian processes with Trend
Long Bai, Krzysztof Debicki, Peng Liu
Let be a centered vector-valued Gaussian process with independent components and continuous trajectories, and $h…