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

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  • J. Aase Nielsen

    (Department of Operations Research, University of Aarhus, Bldg. 530, Ny Munkegade DK-8000 Aarhus C, Denmark.)

  • Klaus Sandmann

    (Department of Statistics, Rheinische Friedrich-Wilhelms-Universit&aauml;t Bonn, Adenauerallee 24-42, D-53113 Bonn, Germany.)

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. This article analyzes 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. The Geneva Papers on Risk and Insurance Theory (1996) 21, 65–102. doi:10.1007/BF00949051

Suggested Citation

  • J. Aase Nielsen & Klaus Sandmann, 1996. "Uniqueness of the Fair Premium for Equity-Linked Life Insurance Contracts," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 21(1), pages 65-102, June.
    • Handle: RePEc:pal:genrir:v:21:y:1996:i:1:p:65-102
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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. 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.
    4. Henri Loubergé, 1998. "Risk and Insurance Economics 25 Years After," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 23(4), pages 540-567, October.
    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. Jensen, Bjarne Astrup & Sørensen, Carsten, 2000. "Paying for minimum interest rate guarantees: Who should compensate who?," Working Papers 2000-1, Copenhagen Business School, Department of Finance.
    7. Hürlimann, Werner, 2010. "Analytical Pricing of the Unit-Linked Endowment with Guarantees and Periodic Premiums," ASTIN Bulletin, Cambridge University Press, vol. 40(2), pages 631-653, November.
    8. 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.
    9. Chen, An, 2005. "Loss Analysis of a Life Insurance Company Applying Discrete-time Risk-minimizing Hedging Strategies," Bonn Econ Discussion Papers 19/2005, University of Bonn, Bonn Graduate School of Economics (BGSE).
    10. Antje B. Mahayni & Klaus Sandmann, 2008. "Return Guarantees with Delayed Payment," German Economic Review, Verein für Socialpolitik, vol. 9(2), pages 207-231, May.
    11. Burnecki, Krzysztof & Pazdan-Siudeja, Liliana, 2008. "Equity-linked insurances and guaranteed annuity options," MPRA Paper 21658, University Library of Munich, Germany.
    12. David R. Ba~nos, 2020. "Life insurance policies with cash flows subject to random interest rate changes," Papers 2012.15541, arXiv.org.
    13. Leunglung Chan & Eckhard Platen, 2016. "Pricing of long dated equity-linked life insurance contracts," Published Paper Series 2016-5, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    14. 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.
    15. Eckhard Platen, 2009. "Real World Pricing of Long Term Contracts," Research Paper Series 262, Quantitative Finance Research Centre, University of Technology, Sydney.

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