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Optimal pension insurance design

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  • Døskeland, Trond M.
  • Nordahl, Helge A.

Abstract

In this paper we analyze how the traditional life and pension contracts with a guaranteed rate of return can be optimized to increase customers' welfare. Given that the contracts have to be priced correctly, we use individuals' preferences to find the preferred design. Assuming CRRA utility, we cannot explain the existence of any form of guarantees. Through numerical solutions we quantify the difference (measured in certainty equivalents) to the preferred Merton solution of direct investments in a fixed proportion of risky and risk free assets. The largest welfare loss seems to come from the fact that guarantees are effective by the end of each year, not only by the expiry of the contract. However, the demand for products with guarantees may be explained through behavioral models. We use cumulative prospect theory as an example, showing that the optimal design is a simple contract with a life-time guarantee and no default option.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Banking & Finance.

Volume (Year): 32 (2008)
Issue (Month): 3 (March)
Pages: 382-392

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Handle: RePEc:eee:jbfina:v:32:y:2008:i:3:p:382-392

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References

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  1. Camerer, Colin F & Ho, Teck-Hua, 1994. "Violations of the Betweenness Axiom and Nonlinearity in Probability," Journal of Risk and Uncertainty, Springer, vol. 8(2), pages 167-96, March.
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  8. Arjan B. Berkelaar & Roy Kouwenberg & Thierry Post, 2004. "Optimal Portfolio Choice under Loss Aversion," The Review of Economics and Statistics, MIT Press, vol. 86(4), pages 973-987, November.
  9. Grosen, Anders & Lochte Jorgensen, Peter, 2000. "Fair valuation of life insurance liabilities: The impact of interest rate guarantees, surrender options, and bonus policies," Insurance: Mathematics and Economics, Elsevier, vol. 26(1), pages 37-57, February.
  10. George Wu & Richard Gonzalez, 1996. "Curvature of the Probability Weighting Function," Management Science, INFORMS, vol. 42(12), pages 1676-1690, December.
  11. Consiglio, Andrea & Saunders, David & Zenios, Stavros A., 2006. "Asset and liability management for insurance products with minimum guarantees: The UK case," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 645-667, February.
  12. R. C. Merton, 1970. "Optimum Consumption and Portfolio Rules in a Continuous-time Model," Working papers 58, Massachusetts Institute of Technology (MIT), Department of Economics.
  13. Tversky, Amos & Kahneman, Daniel, 1992. " Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
  14. Eric Briys & Fran�ois De Varenne, 1994. "Life Insurance in a Contingent Claim Framework: Pricing and Regulatory Implications," The Geneva Risk and Insurance Review, Palgrave Macmillan, vol. 19(1), pages 53-72, June.
  15. Brennan, Michael J. & Schwartz, Eduardo S., 1976. "The pricing of equity-linked life insurance policies with an asset value guarantee," Journal of Financial Economics, Elsevier, vol. 3(3), pages 195-213, June.
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Citations

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Cited by:
  1. Branger, Nicole & Mahayni, Antje & Schneider, Judith C., 2010. "On the optimal design of insurance contracts with guarantees," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 485-492, June.
  2. Johanna Scheller & Jacques Pézier, 2008. "Optimal Investment Strategies and Performance Sharing Rules for Pension Schemes with Minimum Guarantee," ICMA Centre Discussion Papers in Finance icma-dp2008-09, Henley Business School, Reading University, revised Oct 2009.
  3. Døskeland, Trond M. & Nordahl, Helge A., 2006. "Intergenerational Effects of Guaranteed Pension Contracts," Discussion Papers 2006/13, Department of Business and Management Science, Norwegian School of Economics, revised 21 Jun 2007.
  4. Broeders, Dirk & Chen, An, 2010. "Pension regulation and the market value of pension liabilities: A contingent claims analysis using Parisian options," Journal of Banking & Finance, Elsevier, vol. 34(6), pages 1201-1214, June.
  5. Berkelaar, Arjan & Kouwenberg, Roy, 2009. "From boom 'til bust: How loss aversion affects asset prices," Journal of Banking & Finance, Elsevier, vol. 33(6), pages 1005-1013, June.
  6. Mahayni, Antje & Schneider, Judith C., 2012. "Variable annuities and the option to seek risk: Why should you diversify?," Journal of Banking & Finance, Elsevier, vol. 36(9), pages 2417-2428.

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