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

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  • Tsanakas, Andreas

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.

Suggested Citation

  • Tsanakas, Andreas, 2009. "To split or not to split: Capital allocation with convex risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 268-277, April.
  • Handle: RePEc:eee:insuma:v:44:y:2009:i:2:p:268-277
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    References listed on IDEAS

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    Cited by:

    1. Boonen, T.J. & De Waegenaere, A.M.B. & Norde, H.W., 2012. "A Generalization of the Aumann-Shapley Value for Risk Capital Allocation Problems," Discussion Paper 2012-091, Tilburg University, Center for Economic Research.
    2. Hirbod Assa & Manuel Morales & Hassan Omidi Firouzi, 2016. "On the Capital Allocation Problem for a New Coherent Risk Measure in Collective Risk Theory," Risks, MDPI, Open Access Journal, vol. 4(3), pages 1-20, August.
    3. Brunnermeier, Markus K. & Oehmke, Martin, 2013. "Bubbles, Financial Crises, and Systemic Risk," Handbook of the Economics of Finance, Elsevier.
    4. You, Yinping & Li, Xiaohu, 2015. "Functional characterizations of bivariate weak SAI with an application," Insurance: Mathematics and Economics, Elsevier, pages 225-231.
    5. Belles-Sampera, Jaume & Guillén, Montserrat & Santolino, Miguel, 2014. "GlueVaR risk measures in capital allocation applications," Insurance: Mathematics and Economics, Elsevier, pages 132-137.
    6. Urbina, Jilber & Guillén, Montserrat, 2013. "An application of capital allocation principles to operational risk," Working Papers 2072/222201, Universitat Rovira i Virgili, Department of Economics.
    7. van Gulick, Gerwald & De Waegenaere, Anja & Norde, Henk, 2012. "Excess based allocation of risk capital," Insurance: Mathematics and Economics, Elsevier, pages 26-42.
    8. Eduard Kromer & Ludger Overbeck, 2013. "Suitability of Capital Allocations for Performance Measurement," Papers 1301.5497, arXiv.org, revised Jul 2014.
    9. Burren, Daniel, 2013. "Insurance demand and welfare-maximizing risk capital—Some hints for the regulator in the case of exponential preferences and exponential claims," Insurance: Mathematics and Economics, Elsevier, pages 551-568.
    10. Boonen, Tim J. & Tsanakas, Andreas & Wüthrich, Mario V., 2017. "Capital allocation for portfolios with non-linear risk aggregation," Insurance: Mathematics and Economics, Elsevier, pages 95-106.
    11. Guillén, Montserrat & Sarabia, José María & Prieto, Faustino, 2013. "Simple risk measure calculations for sums of positive random variables," Insurance: Mathematics and Economics, Elsevier, pages 273-280.
    12. Xu, Maochao & Mao, Tiantian, 2013. "Optimal capital allocation based on the Tail Mean–Variance model," Insurance: Mathematics and Economics, Elsevier, pages 533-543.
    13. Xu, Maochao & Hu, Taizhong, 2012. "Stochastic comparisons of capital allocations with applications," Insurance: Mathematics and Economics, Elsevier, pages 293-298.
    14. repec:gam:jrisks:v:5:y:2017:i:2:p:31-:d:101685 is not listed on IDEAS
    15. Kaluszka, Marek & Krzeszowiec, Michał, 2012. "Pricing insurance contracts under Cumulative Prospect Theory," Insurance: Mathematics and Economics, Elsevier, pages 159-166.

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