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

*Andreas Tsanakas*

*Insurance: Mathematics and Economics*, 2009, vol. 44, issue 2, 268-277

**Abstract:**
Convex risk measures were introduced by Deprez and Gerber [Deprez, O., Gerber, H.U., 1985. On convex principles of premium calculation. Insurance: Math. Econom. 4 (3), 179-189]. Here the problem of allocating risk capital to subportfolios is addressed, when convex risk measures are used. 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. It is demonstrated that using a convex risk measure for capital allocation can produce an incentive for infinite fragmentation of portfolios.

**Keywords:** Convex; measures; of; risk; Capital; allocation; Aumann-Shapley; value; Inf-convolution (search for similar items in EconPapers)

**Date:** 2009

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**Persistent link:** https://EconPapers.repec.org/RePEc:eee:insuma:v:44:y:2009:i:2:p:268-277

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