Simultaneous Ruin Probability for Two-Dimensional Fractional Brownian Motion Risk Process over Discrete Grid

We derive the asymptotic behavior of the following ruin probability:P∃t∈Gδ:BHt−c1t>q1uBHt−c2t>q2u,H∈01,u→∞,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathrm{P}\left\{\exists t\in G\left(\delta \right):{B}_H(t)-{c}_1t>{q}_1u,{B}_H(t)-{c}_2t>{q}_2u\right\},\kern0.72em H\in \left(0,1\right),u\to \infty, $$\end{document}