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On the optimal product mix in life insurance companies using conditional value at risk

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Author Info

  • Tsai, Jeffrey T.
  • Wang, Jennifer L.
  • Tzeng, Larry Y.

Abstract

This paper proposes a Conditional Value-at-Risk Minimization (CVaRM) approach to optimize an insurer's product mix. By incorporating the natural hedging strategy of Cox and Lin (2007) and the two-factor stochastic mortality model of Cairns et al. (2006b), we calculate an optimize product mix for insurance companies to hedge against the systematic mortality risk under parameter uncertainty. To reflect the importance of required profit, we further integrate the premium loading of systematic risk. We compare the hedging results to those using the duration match method of Wang et al. (forthcoming), and show that the proposed CVaRM approach has a narrower quantile of loss distribution after hedging--thereby effectively reducing systematic mortality risk for life insurance companies.

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Bibliographic Info

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

Volume (Year): 46 (2010)
Issue (Month): 1 (February)
Pages: 235-241

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Handle: RePEc:eee:insuma:v:46:y:2010:i:1:p:235-241

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

Related research

Keywords: Systematic mortality risk Product mix Natural hedging Parameter risk Conditional VaR;

References

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  1. Dahl, Mikkel, 2004. "Stochastic mortality in life insurance: market reserves and mortality-linked insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 35(1), pages 113-136, August.
  2. Eric Stallard, 2006. "Demographic Issues in Longevity Risk Analysis," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(4), pages 575-609.
  3. Samuel H. Cox & Yijia Lin & Shaun Wang, 2006. "Multivariate Exponential Tilting and Pricing Implications for Mortality Securitization," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(4), pages 719-736.
  4. Schrager, David F., 2006. "Affine stochastic mortality," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 81-97, February.
  5. Dahl, Mikkel & Moller, Thomas, 2006. "Valuation and hedging of life insurance liabilities with systematic mortality risk," Insurance: Mathematics and Economics, Elsevier, vol. 39(2), pages 193-217, October.
  6. Andrew J. G. Cairns & David Blake & Kevin Dowd, 2006. "A Two-Factor Model for Stochastic Mortality with Parameter Uncertainty: Theory and Calibration," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(4), pages 687-718.
  7. Alex Cowley & J. David Cummins, 2005. "Securitization of Life Insurance Assets and Liabilities," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 72(2), pages 193-226.
  8. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
  9. Kevin Dowd & David Blake & Andrew J. G. Cairns & Paul Dawson, 2006. "Survivor Swaps," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(1), pages 1-17.
  10. Renshaw, A. E. & Haberman, S., 2003. "Lee-Carter mortality forecasting with age-specific enhancement," Insurance: Mathematics and Economics, Elsevier, vol. 33(2), pages 255-272, October.
  11. Yijia Lin & Samuel H. Cox, 2005. "Securitization of Mortality Risks in Life Annuities," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 72(2), pages 227-252.
  12. Koissi, Marie-Claire & Shapiro, Arnold F. & Hognas, Goran, 2006. "Evaluating and extending the Lee-Carter model for mortality forecasting: Bootstrap confidence interval," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 1-20, February.
  13. Kevin Dowd & David Blake, 2006. "After VaR: The Theory, Estimation, and Insurance Applications of Quantile-Based Risk Measures," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(2), pages 193-229.
  14. David Blake & Andrew Cairns & Kevin Dowd & Richard MacMinn, 2006. "Longevity Bonds: Financial Engineering, Valuation, and Hedging," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(4), pages 647-672.
  15. Deprez, Olivier & Gerber, Hans U., 1985. "On convex principles of premium calculation," Insurance: Mathematics and Economics, Elsevier, vol. 4(3), pages 179-189, July.
  16. Michel Denuit & Pierre Devolder & Anne-Cécile Goderniaux, 2007. "Securitization of Longevity Risk: Pricing Survivor Bonds With Wang Transform in the Lee-Carter Framework," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 74(1), pages 87-113.
  17. M. A. Milevsky & S. D. Promislow & V. R. Young, 2006. "Killing the Law of Large Numbers: Mortality Risk Premiums and the Sharpe Ratio," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(4), pages 673-686.
  18. Biffis, Enrico, 2005. "Affine processes for dynamic mortality and actuarial valuations," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 443-468, December.
  19. Brouhns, Natacha & Denuit, Michel & Vermunt, Jeroen K., 2002. "A Poisson log-bilinear regression approach to the construction of projected lifetables," Insurance: Mathematics and Economics, Elsevier, vol. 31(3), pages 373-393, December.
  20. Kevin Dowd, 2003. "Survivor Bonds: A Comment on Blake and Burrows," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 70(2), pages 339-348.
  21. Helmut Gründl & Thomas Post & Roman N. Schulze, 2006. "To Hedge or Not to Hedge: Managing Demographic Risk in Life Insurance Companies," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(1), pages 19-41.
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Citations

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Cited by:
  1. Katja Hanewald & Thomas Post & Helmut Gründl, 2009. "Stochastic Mortality, Macroeconomic Risks, and Life Insurer Solvency," SFB 649 Discussion Papers SFB649DP2009-015, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  2. Stevens, R.S.P. & De Waegenaere, A.M.B. & Melenberg, B., 2011. "Longevity Risk and Natural Hedge Potential in Portfolios Of Life Insurance Products: The Effect of Investment Risk," Discussion Paper 2011-036, Tilburg University, Center for Economic Research.
  3. Lin, Tzuling & Tsai, Cary Chi-Liang, 2013. "On the mortality/longevity risk hedging with mortality immunization," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 580-596.
  4. David Blake & Christophe Courbage & Richard MacMinn & Michael Sherris, 2011. "Longevity Risk and Capital Markets: The 2010–2011 Update," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan, vol. 36(4), pages 489-500, October.
  5. Huang, Rachel J. & Miao, Jerry C.Y. & Tzeng, Larry Y., 2013. "Does mortality improvement increase equity risk premiums? A risk perception perspective," Journal of Empirical Finance, Elsevier, vol. 22(C), pages 67-77.
  6. Blake, David & Brockett, Patrick & Cox, Samuel & MacMinn, Richard, 2011. "Longevity risk and capital markets: The 2009-2010 update," MPRA Paper 28868, University Library of Munich, Germany.
  7. Wang, Chou-Wen & Huang, Hong-Chih & Hong, De-Chuan, 2013. "A feasible natural hedging strategy for insurance companies," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 532-541.
  8. van Gulick, Gerwald & De Waegenaere, Anja & Norde, Henk, 2012. "Excess based allocation of risk capital," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 26-42.

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