Asymptotics for VaR and CTE of total aggregate losses in a bivariate operational risk cell model

This paper considers a bivariate operational risk cell model, in which the loss severities are modelled by some heavy-tailed and weakly (or strongly) dependent nonnegative random variables, and the frequency processes are described by two arbitrarily dependent general counting processes. In such a model, we establish some asymptotic formulas for the Value-at-Risk and Conditional Tail Expectation of the total aggregate loss. Some simulation studies are also conducted to check the accuracy of the obtained theoretical results via the Monte Carlo method.