Asymptotic results for tail probabilities of sums of dependent and heavy-tailed random variables

Abstract

Let X ₁,X ₂, ... be a sequence of dependent and heavy-tailed random variables with distributions F ₁, F ₂, ... on (−∞,∞), and let τ be a nonnegative integer-valued random variable independent of the sequence {X _k, k ≥ 1}. In this framework, the asymptotic behavior of the tail probabilities of the quantities $S_n = \sum\limits_{k = 1}^n {X_k }$ and $S_{(n)} = \mathop {\max }\limits_{1 \leqslant k \leqslant n} S_k$ for n > 1, and their randomized versions S _τ and S _(τ) are studied. Some applications to the risk theory are presented.

Keywords

Asymptotic tail probability / Copula / Heavy-tailed distribution / Partial sum / Risk process

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