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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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