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The uncertain mortality intensity framework: Pricing and hedging unit-linked life insurance contracts

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  • Li, Jing
  • Szimayer, Alexander

Abstract

We study the valuation and hedging of unit-linked life insurance contracts in a setting where mortality intensity is governed by a stochastic process. We focus on model risk arising from different specifications for the mortality intensity. To do so we assume that the mortality intensity is almost surely bounded under the statistical measure. Further, we restrict the equivalent martingale measures and apply the same bounds to the mortality intensity under these measures. For this setting we derive upper and lower price bounds for unit-linked life insurance contracts using stochastic control techniques. We also show that the induced hedging strategies indeed produce a dynamic superhedge and subhedge under the statistical measure in the limit when the number of contracts increases. This justifies the bounds for the mortality intensity under the pricing measures. We provide numerical examples investigating fixed-term, endowment insurance contracts and their combinations including various guarantee features. The pricing partial differential equation for the upper and lower price bounds is solved by finite difference methods. For our contracts and choice of parameters the pricing and hedging is fairly robust with respect to misspecification of the mortality intensity. The model risk resulting from the uncertain mortality intensity is of minor importance.

Suggested Citation

  • Li, Jing & Szimayer, Alexander, 2011. "The uncertain mortality intensity framework: Pricing and hedging unit-linked life insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 471-486.
  • Handle: RePEc:eee:insuma:v:49:y:2011:i:3:p:471-486 DOI: 10.1016/j.insmatheco.2011.08.001
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    References listed on IDEAS

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    1. Young, Virginia R., 2008. "Pricing life insurance under stochastic mortality via the instantaneous Sharpe ratio," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 691-703, April.
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    5. Dahl, Mikkel, 2004. "Stochastic mortality in life insurance: market reserves and mortality-linked insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 35(1), pages 113-136, August.
    6. Cairns, Andrew J.G. & Blake, David & Dowd, Kevin, 2006. "Pricing Death: Frameworks for the Valuation and Securitization of Mortality Risk," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 36(01), pages 79-120, May.
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    Citations

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    Cited by:

    1. Cristina Ciumas & Diana-Maria Chis, 2015. "A Comparative Analysis Between Unit-Linked Life Insurance And Other Alternative Investments," Annals - Economy Series, Constantin Brancusi University, Faculty of Economics, vol. 3, pages 27-36, June.
    2. Tahir Choulli & Catherine Daveloose & Mich`ele Vanmaele, 2015. "A martingale representation and risk's decomposition with applications: Mortality/longevity risk and securitization," Papers 1510.05858, arXiv.org, revised Jun 2017.
    3. Francesca Biagini & Yinglin Zhang, 2017. "Reduced-form framework and superhedging for payment streams under model uncertainty," Papers 1707.04475, arXiv.org.
    4. repec:eee:insuma:v:76:y:2017:i:c:p:118-134 is not listed on IDEAS
    5. Biagini, Francesca & Zhang, Yinglin, 2016. "Polynomial diffusion models for life insurance liabilities," Insurance: Mathematics and Economics, Elsevier, pages 114-129.
    6. repec:eee:insuma:v:76:y:2017:i:c:p:149-163 is not listed on IDEAS
    7. Francesca Biagini & Yinglin Zhang, 2016. "Polynomial Diffusion Models for Life Insurance Liabilities," Papers 1602.07910, arXiv.org, revised Sep 2016.
    8. Gan, Guojun, 2013. "Application of data clustering and machine learning in variable annuity valuation," Insurance: Mathematics and Economics, Elsevier, pages 795-801.

    More about this item

    Keywords

    Unit-linked life insurance contracts; Mortality model risk; Price bounds; Stochastic control;

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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