An axiomatic characterization of capital allocations of coherent risk measures

Abstract

An axiomatic definition of coherent capital allocations is given. It is shown that coherent capital allocations defined by the proposed axiom system are closely linked to coherent risk measures. More precisely, the associated risk measure of a coherent capital allocation is coherent and, conversely, for every coherent risk measure there exists a coherent capital allocation.

Keywords:

• Capital allocation
• Coherent risk measures

Acknowledgements

The views expressed in this paper are those of the author and do not necessarily reflect the position of Deutsche Bank AG.

Notes

†Recall Euler's well-known rule that states that if f : S → ℝ is positively homogeneous and differentiable at x ∊ S ⊆ ℝ ⁿ we have