Randomly weighted sums of dependent subexponential random variables with applications to risk theory

For any fixed integer n >= 1, let X1,..., Xn be real- valued random variables with a common subexponential distribution, and let.1,...,.n be positive random variables which are bounded above and independent of X1,..., Xn. Under some rather loose conditional dependence assumptions on the primary random variables X1,..., Xn, this paper proves that the asymptotic relations similar to Sigma(n)(i=1)p(theta(i)x(i) > x) hold as x.8, where.1,...,.n are arbitrarily dependent. In particular, it is shown that the above results hold true for X1,..., Xn with certain Samarnov distributions. The obtained results on randomly weighted sums are applied to estimating the finite-time ruin probability in a discrete-time risk model with both insurance and financial risks.