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Uniqueness of the Fair Premium for Equity-Linked Life Insurance Contracts

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Author Info

  • Nielsen, J. Aase
  • Klaus Sandmann

Abstract

An equity-linked life insurance contract combines an endowment life insurance and an investment strategy with a minimum guarantee. The benefit of this contract is determined by the guaranteed amount plus a bonus equal to a call on the portfolio. This bonus is similar to an Asian option. We analyze the relationship between the periodic insurance premium and its proportional share invested into the portfolio. For a general model of the financial risks we show the existence and uniqueness of an insurance premium. Furthermore the premium is strictly increasing and convex as a function of the share invested. An earlier version of this paper was presented under the title Security Linked Life Policies under Stochastic Interest Rates .

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File URL: http://www.wiwi.uni-bonn.de/bgsepapers/bonsfb/bonsfb327.pdf
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Bibliographic Info

Paper provided by University of Bonn, Germany in its series Discussion Paper Serie B with number 327.

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Length: pages
Date of creation: Sep 1995
Date of revision: Mar 1996
Handle: RePEc:bon:bonsfb:327

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Postal: Bonn Graduate School of Economics, University of Bonn, Adenauerallee 24 - 26, 53113 Bonn, Germany
Fax: +49 228 73 6884
Web page: http://www.bgse.uni-bonn.de

Related research

Keywords: Asian option; forward risk adjusted measure; Monte Carlo simulations; life insurance; stochastic interest rates;

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References

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  1. Nielsen, J. Aase & Klaus Sandmann, 1995. "Equity-linked life insurance - a model with stochastic interest rates," Discussion Paper Serie B 291, University of Bonn, Germany, revised Mar 1995.
  2. Vorst, Ton, 1992. "Prices and hedge ratios of average exchange rate options," International Review of Financial Analysis, Elsevier, vol. 1(3), pages 179-193.
  3. Bacinello, Anna Rita & Ortu, Fulvio, 1993. "Pricing equity-linked life insurance with endogenous minimum guarantees," Insurance: Mathematics and Economics, Elsevier, vol. 12(3), pages 245-257, June.
  4. Ho, Thomas S Y & Lee, Sang-bin, 1986. " Term Structure Movements and Pricing Interest Rate Contingent Claims," Journal of Finance, American Finance Association, vol. 41(5), pages 1011-29, December.
  5. Jamshidian, Farshid, 1989. " An Exact Bond Option Formula," Journal of Finance, American Finance Association, vol. 44(1), pages 205-09, March.
  6. Steinar Ekern & Svein-Arne Persson, 1996. "Exotic Unit-Linked Life Insurance Contracts," The Geneva Risk and Insurance Review, Palgrave Macmillan, vol. 21(1), pages 35-63, June.
  7. Turnbull, Stuart M. & Wakeman, Lee Macdonald, 1991. "A Quick Algorithm for Pricing European Average Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 26(03), pages 377-389, September.
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Citations

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Cited by:
  1. Nielsen, J. Aase & Sandmann, Klaus & Schlögl, Erik, 2011. "Equity-linked pension schemes with guarantees," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 547-564.
  2. Chen, An, 2008. "Loss analysis of a life insurance company applying discrete-time risk-minimizing hedging strategies," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1035-1049, June.
  3. Antje B. Mahayni & Klaus Sandmann, 2008. "Return Guarantees with Delayed Payment," German Economic Review, Verein für Socialpolitik, vol. 9, pages 207-231, 05.
  4. Eckhard Platen, 2009. "Real World Pricing of Long Term Contracts," Research Paper Series 262, Quantitative Finance Research Centre, University of Technology, Sydney.
  5. Schrager, David F. & Pelsser, Antoon A.J., 2004. "Pricing Rate of Return Guarantees in Regular Premium Unit Linked Insurance," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 369-398, October.
  6. Boyle, Phelim P. & Hardy, Mary R., 1997. "Reserving for maturity guarantees: Two approaches," Insurance: Mathematics and Economics, Elsevier, vol. 21(2), pages 113-127, November.
  7. 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.
  8. Kevin Fergusson & Eckhard Platen, 2013. "Real World Pricing of Long Term Cash-Linked Annuities and Equity-Linked Annuities with Cash-Linked Guarantees," Research Paper Series 338, Quantitative Finance Research Centre, University of Technology, Sydney.

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