Tail probability of randomly weighted sums of dependent subexponential random variables with applications to risk theory

[摘要] Following the work of Cheng and Cheng (2018) [6], we reexamine the tail probability of randomly weighted sums of dependent subexponential random variables. Precisely speaking, let {X-n, n >= 1} be real-valued and commonly distributed random variables satisfying a general dependence structure proposed in Ko and Tang (2008) [14], and random weights {theta(n), n >= 1} be positive, bounded above and arbitrarily dependent random variables, but independent of {X-n, n >= 1}. Under some mild conditions, we achieve the asymptotic behavior of tail probability for both randomly weighted finite and infinite sums. Finally, an application of the obtained results to a nonstandard continuous-time renewal risk model is proposed. (C) 2019 Elsevier Inc. All rights reserved.

[发布日期] 2019-12-01

[关键词] Randomly weighted sum;Dependence structure;Subexponential distribution;Consistently varying tail;Tail probability