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

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