Simultaneous ruin probability for multivariate gaussian risk model

Let Z(t) = (Z1(t), . . . , Zd(t)) ⊤, t ∈ R where Zi(t), t ∈ R, i = 1, ..., d are mutually independent centered Gaussian processes with continuous sample paths a.s. and stationary increments. For X(t) = AZ(t), t ∈ R, where A is a nonsingular d× d real-valued matrix, u, c ∈ R and T > 0 we derive tight bounds for P { ∃t∈[0,T ] : ∩i=1{Xi(t)− cit > ui} } and find exact asymptotics as (u1, ..., ud) ⊤ = (ua1, ..., uad)⊤ and u → ∞.

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