Tail probability of randomly weighted sums of subexponential random variables under a dependence structure

2012 ◽  
Vol 82 (9) ◽  
pp. 1727-1736 ◽  
Author(s):  
Yang Yang ◽  
Remigijus Leipus ◽  
Jonas Šiaulys
Keyword(s):  
Random Variables ◽  
Tail Probability ◽  
Weighted Sums ◽  
Dependence Structure ◽  
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.

scholarly journals Tails of the Moments for Sums with Dominatedly Varying Random Summands

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 824
Author(s):  
Mantas Dirma ◽  
Saulius Paukštys ◽  
Jonas Šiaulys
Keyword(s):  
Asymptotic Behaviour ◽  
Real Number ◽  
Random Variables ◽  
Nonnegative Real Number ◽  
Weighted Sums ◽  
Dependence Structure ◽  
Randomly Weighted Sums ◽  
Random Weights

The asymptotic behaviour of the tail expectation ?E(Snξ)α?{Snξ>x} is investigated, where exponent α is a nonnegative real number and Snξ=ξ1+…+ξn is a sum of dominatedly varying and not necessarily identically distributed random summands, following a specific dependence structure. It turns out that the tail expectation of such a sum can be asymptotically bounded from above and below by the sums of expectations ?Eξiα?{ξi>x} with correcting constants. The obtained results are extended to the case of randomly weighted sums, where collections of random weights and primary random variables are independent. For illustration of the results obtained, some particular examples are given, where dependence between random variables is modelled in copulas framework.

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