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Optimal Pension Insurance Design

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Author Info

  • Døskeland, Trond M.

    ()
    (Dept. of Finance and Management Science, Norwegian School of Economics and Business Administration)

  • Nordahl, Helge A.

    ()
    (Dept. of Finance and Management Science, Norwegian School of Economics and Business Administration)

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

Paper provided by Department of Business and Management Science, Norwegian School of Economics in its series Discussion Papers with number 2006/14.

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Length: 22 pages
Date of creation: 18 Oct 2006
Date of revision: 21 Jun 2007
Handle: RePEc:hhs:nhhfms:2006_014

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Postal: NHH, Department of Business and Management Science, Helleveien 30, N-5045 Bergen, Norway
Phone: +47 55 95 92 93
Fax: +47 55 95 96 50
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Web page: http://www.nhh.no/en/research-faculty/department-of-business-and-management-science.aspx
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Related research

Keywords: Household Finance; Portfolio Choice; Life and Pension Insurance; Prospect Theory;

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References

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  1. 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.
  2. Francisco J. Gomes, 2005. "Portfolio Choice and Trading Volume with Loss-Averse Investors," The Journal of Business, University of Chicago Press, vol. 78(2), pages 675-706, March.
  3. John Y. Campbell, 2006. "Household Finance," NBER Working Papers 12149, National Bureau of Economic Research, Inc.
  4. George Wu & Richard Gonzalez, 1996. "Curvature of the Probability Weighting Function," Management Science, INFORMS, vol. 42(12), pages 1676-1690, December.
  5. Bjarne Astrup Jensen & Carsten Sørensen, 2001. "Paying for Minimum Interest Rate Guarantees: Who Should Compensate Who?," European Financial Management, European Financial Management Association, vol. 7(2), pages 183-211.
  6. Berkelaar, A.B. & Kouwenberg, R.R.P., 2000. "Optimal portfolio choice under loss aversion," Econometric Institute Research Papers EI 2000-08/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  7. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
  8. 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.
  9. Michael J. Brennan, 1993. "Aspects of Insurance, Intermediation and Finance*," The Geneva Risk and Insurance Review, Palgrave Macmillan, vol. 18(1), pages 7-30, June.
  10. 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.
  11. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  12. 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.
  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. 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.
  15. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
  16. 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.
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Citations

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Cited by:
  1. Trond M D�skeland & Helge A Nordahl, 2008. "Intergenerational Effects of Guaranteed Pension Contracts," The Geneva Risk and Insurance Review, Palgrave Macmillan, vol. 33(1), pages 19-46, June.
  2. 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.
  3. 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.
  4. Dirk Broeders & An Chen, 2008. "Pension regulation and the market value of pension liabilities - a contingent claims analysis using Parisian options," DNB Working Papers 183, Netherlands Central Bank, Research Department.
  5. 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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