## An axiomatic approach to capital allocation.(English)Zbl 1102.91049

Summary: Capital allocation techniques are of central importance in portfolio management and risk-based performance measurement. In this paper we propose an axiom system for capital allocation and analyze its satisfiability and completeness: it is shown that for a given risk measure $$\rho$$ there exists a capital allocation $$\Lambda_\rho$$ that satisfies the main axioms if and only if $$\rho$$ is subadditive and positively homogeneous. Furthermore, it is proved that the axiom system uniquely specifies $$\Lambda_\rho$$. We apply the axiomatization to the most popular risk measures in the finance industry in order to derive explicit capital allocation formulae for these measures.

### MSC:

 91B28 Finance etc. (MSC2000) 91B30 Risk theory, insurance (MSC2010) 91B32 Resource and cost allocation (including fair division, apportionment, etc.)
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### References:

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