Simultaneous ruin probability for two-dimensional fractional Brownian motion risk process over discrete grid, with supplements

Abstract

This paper derives the asymptotic behavior of the following ruin probability $$P\{\exists t\in G(\delta ):B_H(t)-c_{1}t>q_{1}u,B_H(t)-c_{2}t>q_{2}u\},u\to \infty ,$$ where $B_H$ is a standard fractional Brownian motion, $c_1,q_1,c_2,q_2>0$ and $G(\delta )$ denotes a regular grid $\{0,\delta ,2\delta ,...\}$ for some $\delta >0$. The approximation depends on $H$, $\delta$ (only when $H\le 1/2$) and the relations between parameters $c_1,q_1,c_2,q_2$.

21 pages