Frank Harary. A very independent axiom system. The American mathematical monthly, vol. 68 (1961), pp. 159–162.

1974 ◽  
Vol 39 (3) ◽  
pp. 604-604 ◽  
Author(s):  
Donald H. Potts
Keyword(s):  
Axiom System ◽  
Independent Axiom

A Very Independent Axiom System

1961 ◽  
Vol 68 (2) ◽  
pp. 159 ◽  
Author(s):  
Frank Harary
Keyword(s):  
Axiom System ◽  
Independent Axiom

Another Very Independent Axiom System

1961 ◽  
Vol 68 (10) ◽  
pp. 992
Author(s):  
J. W. Ellis
Keyword(s):  
Axiom System ◽  
Independent Axiom

CAPITAL ALLOCATION WITH MULTIVARIATE RISK MEASURES: AN AXIOMATIC APPROACH

2019 ◽  
Vol 34 (2) ◽  
pp. 297-315
Author(s):  
Linxiao Wei ◽  
Yijun Hu
Keyword(s):  
Standard Deviation ◽  
Portfolio Management ◽  
Risk Measures ◽  
Risk Measure ◽  
Axiomatic Approach ◽  
Capital Allocation ◽  
Axiom System ◽  
Multivariate Risk ◽  
Multivariate Risk Measures ◽  
Multivariate Risk Measure

AbstractCapital 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.

scholarly journals Comparing DNR and WWKL

2004 ◽  
Vol 69 (4) ◽  
pp. 1089-1104 ◽  
Author(s):  
Klaus Ambos-Spies ◽  
Bjørn Kjos-Hanssen ◽  
Steffen Lempp ◽  
Theodore A. Slaman
Keyword(s):  
Reverse Mathematics ◽  
Axiom System ◽  
Recursive Functions ◽  
Weak König’S Lemma ◽  
König’S Lemma

Abstract.In Reverse Mathematics, the axiom system DNR. asserting the existence of diagonally non-recursive functions, is strictly weaker than WWKL0 (weak weak König's Lemma).

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