Asymptotic behavior for distortion risk measures in a bidimensional risk model

Consider a bidimensional continuous-time insurance risk model with investments, in which an insurer operates two business lines with a single accident triggering one claim from each line simultaneously, and the price process of investments is described by a geometric Lévy process. Under the framework of bivariate regular variation, we study the tail asymptotic behavior of the distortion risk measure for the aggregate discounted loss of one business line, conditional on the other line suffering a large aggregate discounted loss. Our derived result effectively characterizes the distress spillover effect between the two business lines. We further derive an explicit asymptotic formula for the commonly used conditional expected shortfall risk measure. We also conduct numerical studies to verify the accuracy of our results and examine the sensitivity of key model parameters.