Capital Allocation and Systemic Risk

Abstract

We study (scalar) systemic risk measures in a general framework. This framework embeds the existing approaches of [KOZ16] (first aggregate or axiomatic approach) and [BFFMB20] (first inject capital). It turns out, that even in non trivial situations systemic risk measures of the first inject capital approach can be described by a first aggregate systemic risk measure. Moreover, we study capital allocation rules. We introduce two types, one is connected to the dual representation of the underlying systemic risk measure and the other one is in the spirit of Aumann-Shapley. The canonical ways to this task in the frameworks of [KOZ16] and [BFFMB20] are special cases of our general dual capital allocation rule. In addition, we are able to extend the so called scenario dependent allocation to arbitrary configurations of the system.