To split or not to split: Capital allocation with convex risk measures

Abstract

Convex risk measures were introduced by Deprez and Gerber (1985). Here the problem of allocating risk capital to subportfolios is addressed, when aggregate capital is calculated by a convex risk measure. The Aumann-Shapley value is proposed as an appropriate allocation mechanism. Distortion-exponential measures are discussed extensively and explicit capital allocation formulas are obtained for the case that the risk measure belongs to this family. Finally the implications of capital allocation with a convex risk measure for the stability of portfolios are discussed.

On capital allocation for stochastic arrangement increasing actuarial risks

“…In the literature of actuarial science, the capital allocation has attracted great attention from researchers, and related work could be found in [5], [17], [8], [21], [6], and references therein. Recently, [22] proposed a general loss function in the study of capital allocation for independent or comonotonic risks.…”

Crowded Trades: An Overlooked Systemic Risk for Central Clearing Counterparties

“…The Euleror-gradient rule is the marginal version of this rule (Patrik, Bernegger, and Rüegg, 1999;Tasche, 2000). Finally, the Shapley rule allocates according to Shapley value, a concept from cooperative game theory (Tsanakas, 2009;Tarashev, Borio, and Tsatsaronis, 2009). Brunnermeier and Oehmke (2013, p. 62-63) characterize a good allocation as follows:…”

On the Capital Allocation Problem for a New Coherent Risk Measure in Collective Risk Theory

“…In [22], the authors also study the capital allocation problem using default option with limited liability. Studying the problem for the class of convex risk measures was carried out in [23]. The authors in [24] study the capital allocation problem by introducing the class of weighted risk capital allocations.…”