On the maximum of randomly weighted sums with regularly varying tails

Consider the randomly weighted sums , n=1,2,..., where {Xk,k=1,2,...} is a sequence of independent real-valued random variables with common distribution F, whose right tail is regularly varying with exponent -[alpha]<0, and {[theta]k,k=1,2,...} is a sequence of positive random variables, independent of {Xk,k=1,2,...}. Under a suitable summability condition on the upper endpoints of [theta]k,k=1,2,..., we prove that .

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Year of publication:	2006
Authors:	Chen, Yiqing ; Ng, Kai W. ; Xie, Xiangsheng
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 76.2006, 10, p. 971-975
Publisher:	Elsevier
Keywords:	Asymptotics Regular variation Ruin probability Tail probability

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

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