TMV-Based Capital Allocation for Multivariate Risks

By Maochao Xu

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Abstract

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

Citation

Xu, Maochao, "TMV-Based Capital Allocation for Multivariate Risks," Variance 10:2, 2018, pp. 240-257.

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Mission Statement

Variance (ISSN 1940-6452) is a peer-reviewed journal published by the Casualty Actuarial Society to disseminate work of interest to casualty actuaries worldwide. The focus of Variance is original practical and theoretical research in casualty actuarial science. Significant survey or similar articles are also considered for publication. Membership in the Casualty Actuarial Society is not a prerequisite for submitting papers to the journal and submissions by non-CAS members is encouraged.