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

This paper considers the randomly weighted sums generated by some dependent subexponen- tial 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 proba- bilities 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.