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Optimal capital allocation based on the Tail Mean–Variance model

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  • Xu, Maochao
  • Mao, Tiantian

Abstract

This paper studies capital allocation problems with the aggregate risk exceeding a certain threshold. We propose a novel capital allocation rule based on the Tail Mean–Variance principle. General formulas for the optimal capital allocations are proposed. Explicit formulas for optimal capital allocations are derived for multivariate elliptical distributions. Moreover, we give asymptotic allocation formulas for multivariate regular variation variables. Various numerical examples are given to illustrate the results, and real insurance data is discussed as well.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:53:y:2013:i:3:p:533-543
    DOI: 10.1016/j.insmatheco.2013.08.005
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    References listed on IDEAS

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    1. Zinoviy Landsman & Emiliano Valdez, 2003. "Tail Conditional Expectations for Elliptical Distributions," North American Actuarial Journal, Taylor & Francis Journals, vol. 7(4), pages 55-71.
    2. Li Zhu & Haijun Li, 2012. "Asymptotic Analysis of Multivariate Tail Conditional Expectations," North American Actuarial Journal, Taylor & Francis Journals, vol. 16(3), pages 350-363.
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    4. Asimit, Alexandru V. & Furman, Edward & Tang, Qihe & Vernic, Raluca, 2011. "Asymptotics for risk capital allocations based on Conditional Tail Expectation," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 310-324.
    5. Landsman, Zinoviy, 2010. "On the Tail Mean-Variance optimal portfolio selection," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 547-553, June.
    6. 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.
    7. 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, March.
    8. Xu, Maochao & Hu, Taizhong, 2012. "Stochastic comparisons of capital allocations with applications," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 293-298.
    9. Harry Joe & Haijun Li, 2011. "Tail Risk of Multivariate Regular Variation," Methodology and Computing in Applied Probability, Springer, vol. 13(4), pages 671-693, December.
    10. Valdez, Emiliano A. & Chernih, Andrew, 2003. "Wang's capital allocation formula for elliptically contoured distributions," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 517-532, December.
    11. Furman, Edward & Landsman, Zinoviy, 2006. "Tail Variance Premium with Applications for Elliptical Portfolio of Risks," ASTIN Bulletin, Cambridge University Press, vol. 36(2), pages 433-462, November.
    12. Frostig, Esther & Zaks, Yaniv & Levikson, Benny, 2007. "Optimal pricing for a heterogeneous portfolio for a given risk factor and convex distance measure," Insurance: Mathematics and Economics, Elsevier, vol. 40(3), pages 459-467, May.
    13. Furman, Edward & Landsman, Zinoviy, 2005. "Risk capital decomposition for a multivariate dependent gamma portfolio," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 635-649, December.
    14. Laeven, Roger J. A. & Goovaerts, Marc J., 2004. "An optimization approach to the dynamic allocation of economic capital," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 299-319, October.
    15. Furman, Edward & Zitikis, Ricardas, 2008. "Weighted risk capital allocations," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 263-269, October.
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    Cited by:

    1. Jaume Belles-Sampera & Montserrat Guillen & Miguel Santolino, 2023. "Haircut Capital Allocation as the Solution of a Quadratic Optimisation Problem," Mathematics, MDPI, vol. 11(18), pages 1-17, September.
    2. Cai, Jun & Wang, Ying, 2021. "Optimal capital allocation principles considering capital shortfall and surplus risks in a hierarchical corporate structure," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 329-349.
    3. Righi, Marcelo Brutti & Müller, Fernanda Maria & Moresco, Marlon Ruoso, 2020. "On a robust risk measurement approach for capital determination errors minimization," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 199-211.
    4. Belles-Sampera, Jaume & Guillén, Montserrat & Santolino, Miguel, 2014. "GlueVaR risk measures in capital allocation applications," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 132-137.
    5. Wang, Wei & Xu, Huifu & Ma, Tiejun, 2023. "Optimal scenario-dependent multivariate shortfall risk measure and its application in risk capital allocation," European Journal of Operational Research, Elsevier, vol. 306(1), pages 322-347.
    6. Kamil J. Mizgier & Joseph M. Pasia, 2016. "Multiobjective optimization of credit capital allocation in financial institutions," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 24(4), pages 801-817, December.
    7. Jiang, Chun-Fu & Peng, Hong-Yi & Yang, Yu-Kuan, 2016. "Tail variance of portfolio under generalized Laplace distribution," Applied Mathematics and Computation, Elsevier, vol. 282(C), pages 187-203.
    8. Eini, Esmat Jamshidi & Khaloozadeh, Hamid, 2021. "The tail mean–variance optimal portfolio selection under generalized skew-elliptical distribution," Insurance: Mathematics and Economics, Elsevier, vol. 98(C), pages 44-50.
    9. Kamil J. Mizgier & Joseph M. Pasia & Srinivas Talluri, 2017. "Multiobjective capital allocation for supplier development under risk," International Journal of Production Research, Taylor & Francis Journals, vol. 55(18), pages 5243-5258, September.
    10. Cai, Jun & Wang, Ying & Mao, Tiantian, 2017. "Tail subadditivity of distortion risk measures and multivariate tail distortion risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 105-116.
    11. Wang, Qiyu & Huang, Wenli & Wu, Xin & Zhang, Chao, 2019. "How effective is the tail mean-variance model in the fund of fund selection? An empirical study using various risk measures," Finance Research Letters, Elsevier, vol. 29(C), pages 239-244.

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