Tail asymptotics of randomly weighted sums of dependent strong subexponential random variables

2021 ◽  
Author(s):  
Huan Qian ◽  
Bingzhen Geng ◽  
Shijie Wang
Keyword(s):  
Random Variables ◽  
Weighted Sums ◽  
Tail Asymptotics ◽  
Randomly Weighted Sums

Uniform Estimate for Randomly Weighted Sums of Dependent Subexponential Random Variables

2015 ◽  
Vol 9 (2) ◽  
Author(s):  
Yan Liu ◽  
Qinqin Zhang
Keyword(s):  
Uniform Estimate ◽  
Random Variables ◽  
Weighted Sums ◽  
Weighted Sum ◽  
Tail Asymptotics ◽  
Randomly Weighted Sums

AbstractThis paper obtains the uniform tail asymptotics of the maximum of randomly weighted sum

scholarly journals On the Kesten-type inequality for randomly weighted sums with applications to an operational risk model

Filomat ◽  
2021 ◽  
Vol 35 (6) ◽  
pp. 1879-1888
Author(s):  
Yishan Gong ◽  
Yang Yang ◽  
Jiajun Liu
Keyword(s):  
Value At Risk ◽  
Risk Model ◽  
Cell Model ◽  
Type Inequality ◽  
Random Variables ◽  
Operational Risk ◽  
Weighted Sums ◽  
Asymptotic Formulas ◽  
Tail Probabilities ◽  
Randomly Weighted Sums

This paper considers the randomly weighted sums generated by some dependent subexponential primary random variables and some arbitrarily dependent random weights. To study the randomly weighted sums with infinitely many terms, we establish a Kesten-type upper bound for their tail probabilities in presence of subexponential primary random variables and under a certain dependence among them. Our result extends the study of Chen [5] to the dependent case. As applications, we derive some asymptotic formulas for the tail probability and the Value-at-Risk of total aggregate loss in a multivariate operational risk cell model.

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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