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

Abstract

For any fixed integer , let be real-valued random variables with a common subexponential distribution, and let be positive random variables which are bounded above and independent of . Under some rather loose conditional dependence assumptions on the primary random variables , this paper proves that the asymptotic relationshold as , where are arbitrarily dependent. In particular, it is shown that the above results hold true for 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.