IDEAS home Printed from https://ideas.repec.org/a/bla/jrinsu/v76y2009i3p709-725.html
   My bibliography  Save this article

Optimal Reinsurance Arrangements Under Tail Risk Measures

Author

Listed:
  • Carole Bernard
  • Weidong Tian

Abstract

Regulatory authorities demand insurance companies control their risk exposure by imposing stringent risk management policies. This article investigates the optimal risk management strategy of an insurance company subject to regulatory constraints. We provide optimal reinsurance contracts under different tail risk measures and analyze the impact of regulators' requirements on risk sharing in the reinsurance market. Our results underpin adverse incentives for the insurer when compulsory Value-at-Risk risk management requirements are imposed. But economic effects may vary when regulatory constraints involve other risk measures. Finally, we compare the obtained optimal designs to existing reinsurance contracts and alternative risk transfer mechanisms on the capital market. Copyright (c) The Journal of Risk and Insurance, 2009.

Suggested Citation

  • Carole Bernard & Weidong Tian, 2009. "Optimal Reinsurance Arrangements Under Tail Risk Measures," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(3), pages 709-725.
  • Handle: RePEc:bla:jrinsu:v:76:y:2009:i:3:p:709-725
    as

    Download full text from publisher

    File URL: http://www.blackwell-synergy.com/doi/abs/10.1111/j.1539-6975.2009.01315.x
    File Function: link to full text
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Froot, Kenneth A., 2001. "The market for catastrophe risk: a clinical examination," Journal of Financial Economics, Elsevier, vol. 60(2-3), pages 529-571, May.
    2. Gur Huberman & David Mayers & Clifford W. Smith Jr., 1983. "Optimal Insurance Policy Indemnity Schedules," Bell Journal of Economics, The RAND Corporation, vol. 14(2), pages 415-426, Autumn.
    3. Leippold, Markus & Trojani, Fabio & Vanini, Paolo, 2006. "Equilibrium impact of value-at-risk regulation," Journal of Economic Dynamics and Control, Elsevier, vol. 30(8), pages 1277-1313, August.
    4. Basak, Suleyman & Shapiro, Alexander, 2001. "Value-at-Risk-Based Risk Management: Optimal Policies and Asset Prices," Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 371-405.
    5. J. David Cummins & Olivier Mahul, 2004. "The Demand for Insurance With an Upper Limit on Coverage," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 71(2), pages 253-264.
    6. Arthur Hau, 2006. "The Liquidity Demand for Corporate Property Insurance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(2), pages 261-278.
    7. Froot, Kenneth A. & Stein, Jeremy C., 1998. "Risk management, capital budgeting, and capital structure policy for financial institutions: an integrated approach," Journal of Financial Economics, Elsevier, vol. 47(1), pages 55-82, January.
    8. Gollier, Christian & Schlesinger, Harris, 1996. "Arrow's Theorem on the Optimality of Deductibles: A Stochastic Dominance Approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 359-363, February.
    9. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
    10. Cummins, J. David & Doherty, Neil & Lo, Anita, 2002. "Can insurers pay for the "big one"? Measuring the capacity of the insurance market to respond to catastrophic losses," Journal of Banking & Finance, Elsevier, vol. 26(2-3), pages 557-583, March.
    11. Phelim Boyle & Weidong Tian, 2007. "Portfolio Management With Constraints," Mathematical Finance, Wiley Blackwell, vol. 17(3), pages 319-343.
    12. Cummins, J. David & Lalonde, David & Phillips, Richard D., 2004. "The basis risk of catastrophic-loss index securities," Journal of Financial Economics, Elsevier, vol. 71(1), pages 77-111, January.
    13. Furman, Edward & Landsman, Zinoviy, 2006. "Tail Variance Premium with Applications for Elliptical Portfolio of Risks," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 36(02), pages 433-462, November.
    14. Inui, Koji & Kijima, Masaaki, 2005. "On the significance of expected shortfall as a coherent risk measure," Journal of Banking & Finance, Elsevier, vol. 29(4), pages 853-864, April.
    15. Bruno Jullien & Georges Dionne & Bernard Caillaud, 2000. "Corporate insurance with optimal financial contracting," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 16(1), pages 77-105.
    16. Froot, Kenneth A & Scharfstein, David S & Stein, Jeremy C, 1993. " Risk Management: Coordinating Corporate Investment and Financing Policies," Journal of Finance, American Finance Association, vol. 48(5), pages 1629-1658, December.
    17. Meyer, Jack & Ormiston, Michael B, 1999. "Analyzing the Demand for Deductible Insurance," Journal of Risk and Uncertainty, Springer, vol. 18(3), pages 223-230, October.
    18. Ching-Ping Wang & David Shyu & Hung-Hsi Huang, 2005. "Optimal Insurance Design Under a Value-at-Risk Framework," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 30(2), pages 161-179, December.
    19. Mayers, David & Smith, Clifford W, Jr, 1982. "On the Corporate Demand for Insurance," The Journal of Business, University of Chicago Press, vol. 55(2), pages 281-296, April.
    20. Raviv, Artur, 1979. "The Design of an Optimal Insurance Policy," American Economic Review, American Economic Association, vol. 69(1), pages 84-96, March.
    21. Ching-Ping Wang & David Shyu & Hung-Hsi Huang, 2005. "Optimal Insurance Design Under a Value-at-Risk Framework," The Geneva Papers on Risk and Insurance Theory, Springer;International Association for the Study of Insurance Economics (The Geneva Association), vol. 30(2), pages 161-179, December.
    22. Marek Kaluszka & Andrzej Okolewski, 2008. "An Extension of Arrow's Result on Optimal Reinsurance Contract," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 75(2), pages 275-288.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Heras, Antonio & Balbás, Alejandro & Balbás, Beatriz, 2010. "Stability of the optimal reinsurance with respect to the risk measure," DEE - Working Papers. Business Economics. WB wb100201, Universidad Carlos III de Madrid. Departamento de Economía de la Empresa.
    2. Yuen, Kam Chuen & Liang, Zhibin & Zhou, Ming, 2015. "Optimal proportional reinsurance with common shock dependence," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 1-13.
    3. Lu, ZhiYi & Meng, LiLi & Wang, Yujin & Shen, Qingjie, 2016. "Optimal reinsurance under VaR and TVaR risk measures in the presence of reinsurer’s risk limit," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 92-100.
    4. repec:spr:annopr:v:237:y:2016:i:1:d:10.1007_s10479-014-1584-8 is not listed on IDEAS
    5. Chi, Yichun & Tan, Ken Seng, 2013. "Optimal reinsurance with general premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 180-189.
    6. Wenjun Jiang & Jiandong Ren & Ričardas Zitikis, 2017. "Optimal Reinsurance Policies under the VaR Risk Measure When the Interests of Both the Cedent and the Reinsurer Are Taken into Account," Risks, MDPI, Open Access Journal, vol. 5(1), pages 1-22, February.
    7. Cheung, K.C. & Chong, W.F. & Yam, S.C.P., 2015. "Convex ordering for insurance preferences," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 409-416.
    8. Chi, Yichun & Weng, Chengguo, 2013. "Optimal reinsurance subject to Vajda condition," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 179-189.
    9. Hirbod Assa, 2014. "On Optimal Reinsurance Policy with Distortion Risk Measures and Premiums," Papers 1406.2950, arXiv.org.
    10. Wang, Ching-Ping & Huang, Hung-Hsi, 2016. "Optimal insurance contract under VaR and CVaR constraints," The North American Journal of Economics and Finance, Elsevier, vol. 37(C), pages 110-127.
    11. Sordo, Miguel A., 2009. "Comparing tail variabilities of risks by means of the excess wealth order," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 466-469, December.
    12. Tan, Ken Seng & Weng, Chengguo & Zhang, Yi, 2011. "Optimality of general reinsurance contracts under CTE risk measure," Insurance: Mathematics and Economics, Elsevier, vol. 49(2), pages 175-187, September.
    13. Carole Bernard & Weidong Tian, 2010. "Insurance Market Effects of Risk Management Metrics," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 35(1), pages 47-80, June.
    14. Hirbod Assa, 2015. "Risk management under a prudential policy," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 38(2), pages 217-230, October.
    15. Alejandro Balbas & Beatriz Balbas & Raquel Balbas, 2013. "Optimal Reinsurance: A Risk Sharing Approach," Risks, MDPI, Open Access Journal, vol. 1(2), pages 1-12, August.
    16. Cui, Wei & Yang, Jingping & Wu, Lan, 2013. "Optimal reinsurance minimizing the distortion risk measure under general reinsurance premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 74-85.
    17. Assa, Hirbod, 2015. "On optimal reinsurance policy with distortion risk measures and premiums," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 70-75.
    18. Guerra, Manuel & Centeno, M.L., 2012. "Are quantile risk measures suitable for risk-transfer decisions?," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 446-461.
    19. Balbás, Alejandro & Balbás, Beatriz & Heras, Antonio, 2011. "Stable solutions for optimal reinsurance problems involving risk measures," European Journal of Operational Research, Elsevier, vol. 214(3), pages 796-804, November.
    20. Hu, Xiang & Yang, Hailiang & Zhang, Lianzeng, 2015. "Optimal retention for a stop-loss reinsurance with incomplete information," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 15-21.
    21. Carole Bernard & Shaolin Ji & Weidong Tian, 2013. "An optimal insurance design problem under Knightian uncertainty," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 36(2), pages 99-124, November.
    22. Boonen, Tim J. & Tan, Ken Seng & Zhuang, Sheng Chao, 2016. "The role of a representative reinsurer in optimal reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 196-204.
    23. Chi, Yichun, 2012. "Optimal reinsurance under variance related premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 310-321.
    24. repec:eee:insuma:v:77:y:2017:i:c:p:24-37 is not listed on IDEAS

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:jrinsu:v:76:y:2009:i:3:p:709-725. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wiley-Blackwell Digital Licensing) or (Christopher F. Baum). General contact details of provider: http://edirc.repec.org/data/ariaaea.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.