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Multivariate risk measures based on conditional expectation and systemic risk for Exponential Dispersion Models

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  • Shushi, Tomer
  • Yao, Jing

Abstract

Exponential dispersion models are well used and studied in quantitative risk management and actuarial science. One of the main interests is the risk measurement analysis of such models when facing extreme loss events. In this paper, we propose two multivariate risk measures based on conditional expectation and derive the explicit formulae for exponential dispersion models. In particular, our multivariate risk measures could facilitate a systemic risk measure with explicit expressions for exponential dispersion models subject to any pre-specified “systemic event.” We provide two numerical examples based on practical data to show the advantages of our approach in the context of exponential dispersion models.

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  • Shushi, Tomer & Yao, Jing, 2020. "Multivariate risk measures based on conditional expectation and systemic risk for Exponential Dispersion Models," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 178-186.
    • Handle: RePEc:eee:insuma:v:93:y:2020:i:c:p:178-186
    DOI: 10.1016/j.insmatheco.2020.04.014
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    1. Torres Díaz, Raúl Andrés & Lillo Rodríguez, Rosa Elvira & Laniado Rodas, Henry, 2015. "A Directional Multivariate Value at Risk," DES - Working Papers. Statistics and Econometrics. WS ws1501, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. Viral V. Acharya & Lasse H. Pedersen & Thomas Philippon & Matthew Richardson, 2017. "Measuring Systemic Risk," Review of Financial Studies, Society for Financial Studies, vol. 30(1), pages 2-47.
    3. Cousin, Areski & Di Bernardino, Elena, 2014. "On multivariate extensions of Conditional-Tail-Expectation," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 272-282.
    4. Dhaene, Jan & Laeven, Roger J.A. & Zhang, Yiying, 2022. "Systemic risk: Conditional distortion risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 102(C), pages 126-145.
    5. Zhou, Ming & Dhaene, Jan & Yao, Jing, 2018. "An approximation method for risk aggregations and capital allocation rules based on additive risk factor models," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 92-100.
    6. Landsman, Zinoviy & Valdez, Emiliano A., 2005. "Tail Conditional Expectations for Exponential Dispersion Models," ASTIN Bulletin, Cambridge University Press, vol. 35(1), pages 189-209, May.
    7. Areski Cousin & Elena Di Bernadino, 2013. "On Multivariate Extensions of Value-at-Risk," Working Papers hal-00638382, HAL.
    8. Dickson,David C. M., 2016. "Insurance Risk and Ruin," Cambridge Books, Cambridge University Press, number 9781107154605.
    9. Smyth, Gordon K. & Jørgensen, Bent, 2002. "Fitting Tweedie's Compound Poisson Model to Insurance Claims Data: Dispersion Modelling," ASTIN Bulletin, Cambridge University Press, vol. 32(1), pages 143-157, May.
    10. Roger J. A. Laeven & Mitja Stadje, 2013. "Entropy Coherent and Entropy Convex Measures of Risk," Mathematics of Operations Research, INFORMS, vol. 38(2), pages 265-293, May.
    11. Landsman, Zinoviy & Makov, Udi & Shushi, Tomer, 2016. "Multivariate tail conditional expectation for elliptical distributions," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 216-223.
    12. Cousin, Areski & Di Bernardino, Elena, 2013. "On multivariate extensions of Value-at-Risk," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 32-46.
    13. de Jong,Piet & Heller,Gillian Z., 2008. "Generalized Linear Models for Insurance Data," Cambridge Books, Cambridge University Press, number 9780521879149.
    14. Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and Dynamic Convex Risk Measures," SFB 649 Discussion Papers SFB649DP2005-006, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    15. Elyés Jouini & Moncef Meddeb & Nizar Touzi, 2004. "Vector-valued coherent risk measures," Finance and Stochastics, Springer, vol. 8(4), pages 531-552, November.
    16. Ra'ul Torres & Rosa E. Lillo & Henry Laniado, 2015. "A Directional Multivariate Value at Risk," Papers 1502.00908, arXiv.org.
    17. Torres, Raúl & Lillo, Rosa E. & Laniado, Henry, 2015. "A directional multivariate value at risk," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 111-123.
    18. Christian Brownlees & Robert F. Engle, 2017. "SRISK: A Conditional Capital Shortfall Measure of Systemic Risk," Review of Financial Studies, Society for Financial Studies, vol. 30(1), pages 48-79.
    19. Valdez, Emiliano A. & Dhaene, Jan & Maj, Mateusz & Vanduffel, Steven, 2009. "Bounds and approximations for sums of dependent log-elliptical random variables," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 385-397, June.
    20. Fima Klebaner & Zinoviy Landsman & Udi Makov & Jing Yao, 2017. "Optimal portfolios with downside risk," Quantitative Finance, Taylor & Francis Journals, vol. 17(3), pages 315-325, March.
    21. Hélène Cossette & Mélina Mailhot & Étienne Marceau & Mhamed Mesfioui, 2016. "Vector-Valued Tail Value-at-Risk and Capital Allocation," Methodology and Computing in Applied Probability, Springer, vol. 18(3), pages 653-674, September.
    22. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    23. Areski Cousin & Elena Di Bernadino, 2011. "On Multivariate Extensions of Value-at-Risk," Papers 1111.1349, arXiv.org, revised Apr 2013.
    24. repec:dau:papers:123456789/353 is not listed on IDEAS
    25. 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.
    26. Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and dynamic convex risk measures," Finance and Stochastics, Springer, vol. 9(4), pages 539-561, October.
    27. Kleinow, Jacob & Moreira, Fernando & Strobl, Sascha & Vähämaa, Sami, 2017. "Measuring systemic risk: A comparison of alternative market-based approaches," Finance Research Letters, Elsevier, vol. 21(C), pages 40-46.
    28. Blough, David K. & Madden, Carolyn W. & Hornbrook, Mark C., 1999. "Modeling risk using generalized linear models," Journal of Health Economics, Elsevier, vol. 18(2), pages 153-171, April.
    29. Francesca Biagini & Jean‐Pierre Fouque & Marco Frittelli & Thilo Meyer‐Brandis, 2019. "A unified approach to systemic risk measures via acceptance sets," Mathematical Finance, Wiley Blackwell, vol. 29(1), pages 329-367, January.
    30. Alai, Daniel H. & Landsman, Zinoviy & Sherris, Michael, 2015. "A multivariate Tweedie lifetime model: Censoring and truncation," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 203-213.
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    Cited by:

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    3. Li, Jinzhu, 2022. "Asymptotic analysis of a dynamic systemic risk measure in a renewal risk model," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 38-56.
    4. Mohammed, Nawaf & Furman, Edward & Su, Jianxi, 2021. "Can a regulatory risk measure induce profit-maximizing risk capital allocations? The case of conditional tail expectation," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 425-436.
    5. Baishuai Zuo & Chuancun Yin, 2022. "Doubly truncated moment risk measures for elliptical distributions," Papers 2203.01091, arXiv.org.
    6. Shaul K. Bar-Lev, 2021. "On the Notion of Reproducibility and Its Full Implementation to Natural Exponential Families," Mathematics, MDPI, vol. 9(13), pages 1-11, July.
    7. Nawaf Mohammed & Edward Furman & Jianxi Su, 2021. "Can a regulatory risk measure induce profit-maximizing risk capital allocations? The case of Conditional Tail Expectation," Papers 2102.05003, arXiv.org, revised Aug 2021.
    8. Baishuai Zuo & Chuancun Yin & Jing Yao, 2023. "Multivariate range Value-at-Risk and covariance risk measures for elliptical and log-elliptical distributions," Papers 2305.09097, arXiv.org.

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    More about this item

    Keywords

    Multivariate risk measures; Conditional expectation; Systemic risks; Capital allocation; Exponential dispersion models;
    All these keywords.

    JEL classification:

    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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