A note on the max-sum equivalence of randomly weighted sums of heavy-tailed random variables
Articles
Yang Yang
Southeast University, China
Kaiyong Wang
Southeast University, China
Remigijus Leipus
Vilnius University, Lithuania
Jonas Šiaulys
Vilnius University, Lithuania
Published 2013-10-25
https://doi.org/10.15388/NA.18.4.13976
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Keywords

long-tailed distribution
randomly weighted sum
max-sum equivalence

How to Cite

Yang Y., Wang K., Leipus R. and Šiaulys J. (2013) “A note on the max-sum equivalence of randomly weighted sums of heavy-tailed random variables”, Nonlinear Analysis: Modelling and Control, 18(4), pp. 519-525. doi: 10.15388/NA.18.4.13976.

Abstract

This paper investigates the asymptotic behavior for the tail probability of the randomly weighted sums k=1nθkXk and their maximum, where the random variables Xk and the random weights θk follow a certain dependence structure proposed by Asimit and Badescu [1] and Li et al. [2]. The obtained results can be used to obtain asymptotic formulas for ruin probability in the insurance risk models with discounted factors.

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