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

Tsanakas, A. (2009). To split or not to split: capital allocation with convex risk measures. Insurance: Mathematics and Economics, 44(2), pp. 268-277. doi: 10.1016/j.insmatheco.2008.03.007


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.

Publication Type: Article
Additional Information: NOTICE: this is the author’s version of a work that was accepted for publication in <Journal title>. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Insurance: Mathematics and Economics, Volume 44, Issue 2, April 2009, Pages 268–277,
Publisher Keywords: Convex measures of risk; Capital allocation; Aumann–Shapley value; Inf-convolution
Subjects: H Social Sciences > HF Commerce
Departments: Bayes Business School > Actuarial Science & Insurance
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