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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. 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.
    2. 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.
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    Cited by:

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    4. Ruß, Jochen & Schelling, Stefan, 2021. "Return smoothing in life insurance from a client perspective," Insurance: Mathematics and Economics, Elsevier, vol. 101(PA), pages 91-106.
    5. Andreas Reuß & Jochen Ruß & Jochen Wieland, 2016. "Participating Life Insurance Products with Alternative Guarantees: Reconciling Policyholders’ and Insurers’ Interests," Risks, MDPI, vol. 4(2), pages 1-18, May.
    6. 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.
    7. 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.
    8. 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.
    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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