Consider a bidimensional risk model with two geometric Lévy price processes and dependent heavy-tailed claims, in which we allow arbitrary dependence structures between the two claim-number processes generated by two kinds of businesses, and between the two geometric Lévy price processes. Under the assumption that the claims have consistently varying tails, the asymptotics for the infinite-time and finite-time ruin probabilities are derived.

Systemic risk (SR) is considered as the risk of collapse of an entire system, which has played a significant role in explaining the recent financial turmoils from the insurance and financial industries. We consider the asymptotic behavior of the SR for portfolio losses in the model allowing for heavy-tailed primary losses, which are equipped with a wide type of dependence structure. This risk model provides an ideal framework for addressing both heavy-tailedness and dependence. As some extensions, several simulation experiments are conducted, where an insurance application of the asymptotic characterization to the determination and approximation of related SR capital has been proposed, based on the SR measure.

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.