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

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  • Tsanakas, Andreas
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    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 44 (2009)
    Issue (Month): 2 (April)
    Pages: 268-277

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    Handle: RePEc:eee:insuma:v:44:y:2009:i:2:p:268-277

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    Web page: http://www.elsevier.com/locate/inca/505554

    Related research

    Keywords: Convex measures of risk Capital allocation Aumann-Shapley value Inf-convolution;

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    1. Jan Dhaene & Andreas Tsanakas & Emiliano A. Valdez & Steven Vanduffel, 2012. "Optimal Capital Allocation Principles," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 79(1), pages 1-28, 03.
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    Cited by:
    1. Kaluszka, Marek & Krzeszowiec, Michał, 2012. "Pricing insurance contracts under Cumulative Prospect Theory," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 159-166.
    2. Guillén, Montserrat & Sarabia, José María & Prieto, Faustino, 2013. "Simple risk measure calculations for sums of positive random variables," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 273-280.
    3. Eduard Kromer & Ludger Overbeck, 2013. "Suitability of Capital Allocations for Performance Measurement," Papers 1301.5497, arXiv.org, revised Jul 2014.
    4. Gulick, G. van & De Waegenaere, A.M.B. & Norde, H.W., 2010. "Excess Based Allocation of Risk Capital," Discussion Paper 2010-123, Tilburg University, Center for Economic Research.
    5. 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, vol. 53(3), pages 551-568.
    6. Xu, Maochao & Mao, Tiantian, 2013. "Optimal capital allocation based on the Tail Mean–Variance model," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 533-543.
    7. Markus K. Brunnermeier & Martin Oehmke, 2012. "Bubbles, Financial Crises, and Systemic Risk," NBER Working Papers 18398, National Bureau of Economic Research, Inc.
    8. Albert J. Menkveld, 2014. "Crowded Trades: An Overlooked Systemic Risk for Central Clearing Counterparties," Tinbergen Institute Discussion Papers 14-065/IV/DSF75, Tinbergen Institute.
    9. Xu, Maochao & Hu, Taizhong, 2012. "Stochastic comparisons of capital allocations with applications," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 293-298.
    10. 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.

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