Abstract
In the insurance and actuary literature, the topic of capital allocation is extremely important and has attracted considerable interest recently. This issue has been made even more relevant by the increased regulatory attention to capital requirements following the Credit Crisis of 2008, and the developing requirements for the Own Risk and Solvency Assessment (ORSA) process. Understanding the nature of risks is a necessary step toward optimal capital allocations. Although there exists an extensive amount of literature on this subject, most of the discussion has only focused on the magnitude of risks, which ignores the variability of risks, an important factor for capital allocations. In this talk, we discuss the capital allocation based on the Tail Mean-Variance (TMV) principle for multivariate risks. The new model would not only allow the decision-makers to minimize the magnitude but also to penalize the variability of total tail risk under a very general framework. In particular, we study both the tail and dependence effect on the optimal capital allocation. General formulas based on TMV models for optimal capital allocations are derived. We will also discuss the optimal capital allocation when the risks are from multivariate families of heavy-tailed distributions. Some numerical examples are given to illustrate the results.