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Optimal Reinsurance Arrangements Under Tail Risk Measures

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  • 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.

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, September.
    • Handle: RePEc:bla:jrinsu:v:76:y:2009:i:3:p:709-725
    DOI: 10.1111/j.1539-6975.2009.01315.x
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    1. 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.
    2. 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, June.
    3. Phelim Boyle & Weidong Tian, 2007. "Portfolio Management With Constraints," Mathematical Finance, Wiley Blackwell, vol. 17(3), pages 319-343, July.
    4. Christian Gollier & Harris Schlesinger, 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.
    5. 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.
    6. 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.
    7. Basak, Suleyman & Shapiro, Alexander, 2001. "Value-at-Risk-Based Risk Management: Optimal Policies and Asset Prices," The Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 371-405.
    8. 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, June.
    9. 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.
    10. 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.
    11. J. David Cummins & Olivier Mahul, 2004. "The demand for insurance with an upper limit on coverage," Post-Print hal-01952122, HAL.
    12. 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, June.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. 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.
    21. 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.
    22. Raviv, Artur, 1979. "The Design of an Optimal Insurance Policy," American Economic Review, American Economic Association, vol. 69(1), pages 84-96, March.
    23. 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.
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