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Risk analysis and valuation of life insurance contracts: Combining actuarial and financial approaches

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  • Graf, Stefan
  • Kling, Alexander
  • Ruß, Jochen

Abstract

In this paper, we analyze traditional (i.e. not unit-linked) participating life insurance contracts with a guaranteed interest rate and surplus participation. We consider three different surplus distribution models and an asset allocation that consists of money market, bonds with different maturities, and stocks. In this setting, we combine actuarial and financial approaches by selecting a risk minimizing asset allocation (under the real world measure ) and distributing terminal surplus such that the contract value (under the pricing measure ) is fair. We prove that this strategy is always possible unless the insurance contracts introduce arbitrage opportunities in the market. We then analyze differences between the different surplus distribution models and investigate the impact of the selected risk measure on the risk minimizing portfolio.

Suggested Citation

  • Graf, Stefan & Kling, Alexander & Ruß, Jochen, 2011. "Risk analysis and valuation of life insurance contracts: Combining actuarial and financial approaches," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 115-125, July.
    • Handle: RePEc:eee:insuma:v:49:y:2011:i:1:p:115-125
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    References listed on IDEAS

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    1. Gatzert, Nadine, 2008. "Asset management and surplus distribution strategies in life insurance: An examination with respect to risk pricing and risk measurement," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 839-849, April.
    2. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    3. Nadine Gatzert & Alexander Kling, 2007. "Analysis of Participating Life Insurance Contracts: A Unification Approach," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 74(3), pages 547-570, September.
    4. Alexander Kling & Andreas Richter & Jochen Ruß, 2007. "The Impact of Surplus Distribution on the Risk Exposure of With Profit Life Insurance Policies Including Interest Rate Guarantees," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 74(3), pages 571-589, September.
    5. Bauer, Daniel & Kiesel, Rudiger & Kling, Alexander & Ru[ss], Jochen, 2006. "Risk-neutral valuation of participating life insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 39(2), pages 171-183, October.
    6. Barbarin, Jerome & Devolder, Pierre, 2005. "Risk measure and fair valuation of an investment guarantee in life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 37(2), pages 297-323, October.
    7. 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.
    8. Kling, Alexander & Richter, Andreas & Ru[ss], Jochen, 2007. "The interaction of guarantees, surplus distribution, and asset allocation in with-profit life insurance policies," Insurance: Mathematics and Economics, Elsevier, vol. 40(1), pages 164-178, January.
    9. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    10. 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 637-654, May-June.
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    Cited by:

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    4. Daliana Luca & Hato Schmeiser & Florian Schreiber, 2023. "Investment guarantees in financial products: an analysis of consumer preferences," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 48(4), pages 906-940, October.
    5. Eling, Martin & Holder, Stefan, 2013. "The value of interest rate guarantees in participating life insurance contracts: Status quo and alternative product design," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 491-503.
    6. Bohnert, Alexander & Gatzert, Nadine, 2012. "Analyzing surplus appropriation schemes in participating life insurance from the insurer’s and the policyholder’s perspective," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 64-78.
    7. Goecke, Oskar, 2013. "Pension saving schemes with return smoothing mechanism," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 678-689.
    8. Catherine Donnelly, 2017. "A Discussion of a Risk-Sharing Pension Plan," Risks, MDPI, vol. 5(1), pages 1-20, February.
    9. Hieber, Peter, 2017. "Cliquet-style return guarantees in a regime switching Lévy model," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 138-147.

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