Capital allocation rules and generalized collapse to the mean
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Abstract
In the context of capital allocation principles for (not necessarily coherent)
risk measures, we derive - under mild conditions - some representation results
as ''collapse to the mean" in a generalized sense. This approach is related to
the well-known Gradient allocation and allows to extend a result of Kalkbrener
(Theorem 4.3 in [27]) to a non-differentiable setting as well as to more general
capital allocation rules and risk measures