scholarly journals Approximation of the tail probability of randomly weighted sums of dependent random variables with dominated variation

2011 ◽  
Vol 376 (1) ◽  
pp. 365-372 ◽  
Author(s):  
Lan Yi ◽  
Yu Chen ◽  
Chun Su
Keyword(s):  
Random Variables ◽  
Tail Probability ◽  
Weighted Sums ◽  
Dependent Random Variables ◽  
Dominated Variation ◽  
Randomly Weighted Sums

A note on the max-sum equivalence of randomly weighted sums of heavy-tailed random variables

2013 ◽  
Vol 18 (4) ◽  
pp. 519-525 ◽  
Author(s):  
Yang Yang ◽  
Kaiyong Wang ◽  
Remigijus Leipus ◽  
Jonas Šiaulys
Keyword(s):  
Random Variables ◽  
Tail Probability ◽  
Weighted Sums ◽  
Asymptotic Formulas ◽  
Dependence Structure ◽  
Insurance Risk ◽  
Risk Models ◽  
Randomly Weighted Sums ◽  
Random Weights ◽  
Heavy Tailed

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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