38 citations · 61 across the 10 of their papers we have counts for
10 papers
Derivatives of sup-functionals of fractional Brownian motion evaluated at H=1/2
Krzysztof Bisewski, Krzysztof Dębicki, Tomasz Rolski
We consider a family of sup-functionals of (drifted) fractional Brownian motion with Hurst parameter . This family includes, but is not limited to: expected value of the…
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…
Fluctuation theory for level-dependent Lévy risk processes
Irmina Czarna, José-Luis Pérez, Tomasz Rolski +1
A level-dependent Lévy process solves the stochastic differential equation , where is a spectrally negative Lévy process. A special case is a multi-re…
Two-dimensional ruin probability for subexponential claim size
Sergey Foss, Dmitry Korshunov, Zbigniew Palmowski +1
We analyse the asymptotics of ruin probabilities of two insurance companies (or two branches of the same company) that divide between them both claims and premia in some specified…
Extremal behaviour of hitting a cone by correlated Brownian motion with drift
Krzysztof Dȩbicki, Enkelejd Hashorva, Lanpeng Ji +1
This paper derives an exact asymptotic expression for \[ \mathbb{P}_{\mathbf{x}_u}\{\exists_{t\ge0} \mathbf{X}(t)- \boldsymbolμt\in \mathcal{U} \}, \ \ {\rm as}\ \ u\to\infty, \] w…