AN AXIOMATIC APPROACH TO CAPITAL ALLOCATION

Michael Kalkbrener

Mathematical Finance, 2005, vol. 15, issue 3, 425-437

Abstract: 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 ρ there exists a capital allocation Λρ that satisfies the main axioms if and only if ρ is subadditive and positively homogeneous. Furthermore, it is proved that the axiom system uniquely specifies Λρ. 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.

Date: 2005
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