On the Subaddivity of Tail Value at Risk: An Investigation with Copulas

In this paper, we compare the point of view of the regulator and the investors about the required solvency level of an insurance company. We assume that the required solvency level is determined using the Tail Value at Risk and analyze the diversification benefit, both on the required capital and on the residual risk, when merging risks. To describe the dependence structure, we use a range of various copulas. This allows us to judge whether or not the Tail Value at Risk is too subadditive under a wide range of conditions. Furthermore, we discuss the effect of different copulas on the diversification possibilities.