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AN AXIOMATIC APPROACH TO CAPITAL ALLOCATION
Author(s) -
Kalkbrener Michael
Publication year - 2005
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.2005.00227.x
Subject(s) - subadditivity , axiom , capital allocation line , axiomatic system , mathematical economics , capital (architecture) , completeness (order theory) , portfolio , economics , measure (data warehouse) , risk measure , capital requirement , mathematics , econometrics , actuarial science , microeconomics , computer science , finance , discrete mathematics , profit (economics) , mathematical analysis , geometry , archaeology , database , incentive , history
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 Λ ρ 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 Λ ρ . 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.