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{there exists t is an element of G(delta) : B-H(t) - c(1)t > q(1)u, B-H(t) - c(2)t > q(2)u}, H is an element of(0, 1), u -> infinity, where B-H is a standard fractional Brownian motion, c(1), q(1), c(2), q(2)> 0, and G(delta) denotes the regular grid {0, delta, 2 delta, . . . } for some delta > 0. The approximation depends on H, delta (only when H <= 1/2) and the relations between parameters c(1), q(1), c(2), q(2).