On large excursions probabilities for Gaussian copula vector processes. Applications in reliability and finance

Abstract

We study an asymptotic behavior of the ruin probability P( max t∈[0,T] Q n (t) > x T ), t = 0,1,2,..., for T = 0 and large x = x0 (instant ruin probability) and for large both T and x T (global ruin probability). The random process Qn(t) models portfolio Qn(t) = ∑n i=1 λiXi(t), where Xi(t),i = 1,...,n, are independent random sequences, they can be interpreted as the financial loss amount in time claimed from the ith direct insurer or as reliability index of components of a technical system. Weights λi, i = 1,...n, are the proportionality factors of the risks being shared. It is assumed that the risks Xi(t), i = 1,...,n, are Weibull like in a sense that they are similar to Weibull ones in terms of the probability of producing large values.