TMV-Based Capital Allocation for Multivariate Risks
By Maochao Xu
This paper studies a novel capital allocation framework based on the tail mean-variance (TMV) principle for multivariate risks. The new capital allocation model has many intriguing properties, such as controlling the magnitude and variability of tail risks simultaneously. General formulas for optimal capital allocations are discussed according to the semideviation distance measure. In particular, we discuss the optimal capital allocation for comonotonic risks, and risks from multivariate elliptical distribution and multivariate skew-t distribution. Some numerical examples are given to illustrate the results, and real data from an insurance company is analyzed as well.
Keywords: Capital allocation, Lagrange multiplier, mean-variance, skew-t distribution, tail risks