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CAPITAL ALLOCATION WITH MULTIVARIATE RISK MEASURES: AN AXIOMATIC APPROACH

Published online by Cambridge University Press:  06 March 2019

Linxiao Wei  and
Yijun Hu
Linxiao Wei
Affiliation:
College of Science, Wuhan University of Technology, Wuhan, Hubei430070 People's Republic of China E-mail: [email protected]
Yijun Hu
Affiliation:
School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei430072 People's Republic of China E-mail: [email protected]
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Abstract

Capital allocation is of central importance in portfolio management and risk-based performance measurement. Capital allocations for univariate risk measures have been extensively studied in the finance literature. In contrast to this situation, few papers dealt with capital allocations for multivariate risk measures. In this paper, we propose an axiom system for capital allocation with multivariate risk measures. We first recall the class of the positively homogeneous and subadditive multivariate risk measures, and provide the corresponding representation results. Then it is shown that for a given positively homogeneous and subadditive multivariate risk measure, there exists a capital allocation principle. Furthermore, the uniqueness of the capital allocation principe is characterized. Finally, examples are also given to derive the explicit capital allocation principles for the multivariate risk measures based on mean and standard deviation, including the multivariate mean-standard-deviation risk measures.

Keywords

capital allocation principle(financial) portfoliomultivariate risk measurepositive homogeneitysubadditivity
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 34 , Issue 2 , April 2020 , pp. 297 - 315
Copyright
Copyright © Cambridge University Press 2019

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