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Polynomial diffusion models for life insurance liabilities

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  • Biagini, Francesca
  • Zhang, Yinglin

Abstract

In this paper we study the pricing and hedging problem of a portfolio of life insurance products under the benchmark approach, where the reference market is modelled as driven by a state variable following a polynomial diffusion on a compact state space. Such a model can be used to guarantee not only the positivity of the OIS short rate and the mortality intensity, but also the possibility of approximating both pricing formula and hedging strategy of a large class of life insurance products by explicit formulas.

Suggested Citation

  • Biagini, Francesca & Zhang, Yinglin, 2016. "Polynomial diffusion models for life insurance liabilities," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 114-129.
    • Handle: RePEc:eee:insuma:v:71:y:2016:i:c:p:114-129
    DOI: 10.1016/j.insmatheco.2016.08.008
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    References listed on IDEAS

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    1. Eckhard Platen, 2004. "A Benchmark Framework for Risk Management," World Scientific Book Chapters, in: Jiro Akahori & Shigeyoshi Ogawa & Shinzo Watanabe (ed.), Stochastic Processes And Applications To Mathematical Finance, chapter 15, pages 305-335, World Scientific Publishing Co. Pte. Ltd..
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    7. Francesca Biagini & Alessandra Cretarola & Eckhard Platen, 2012. "Local Risk-Minimization under the Benchmark Approach," Papers 1210.2337, arXiv.org.
    8. Eckhard Platen, 2004. "Diversified Portfolios with Jumps in a Benchmark Framework," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 11(1), pages 1-22, March.
    9. Jarner, Søren Fiig & Kryger, Esben Masotti, 2011. "Modelling Adult Mortality in Small Populations: The Saint Model," ASTIN Bulletin, Cambridge University Press, vol. 41(2), pages 377-418, November.
    10. Farshid Jamshidian, 2004. "Valuation of credit default swaps and swaptions," Finance and Stochastics, Springer, vol. 8(3), pages 343-371, August.
    11. 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.
    12. Damir Filipović & Martin Larsson, 2016. "Polynomial diffusions and applications in finance," Finance and Stochastics, Springer, vol. 20(4), pages 931-972, October.
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    14. Ke Du & Eckhard Platen, 2011. "Three-Benchmarked Risk Minimization for Jump Diffusion Markets," Research Paper Series 296, Quantitative Finance Research Centre, University of Technology, Sydney.
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    Citations

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    Cited by:

    1. Xi Kleisinger-Yu & Vlatka Komaric & Martin Larsson & Markus Regez, 2019. "A multi-factor polynomial framework for long-term electricity forwards with delivery period," Papers 1908.08954, arXiv.org, revised Jun 2020.
    2. Francesca Biagini & Yinglin Zhang, 2018. "Extended Reduced-Form Framework for Non-Life Insurance," Papers 1802.07741, arXiv.org, revised Jun 2022.
    3. Christa Cuchiero & Sara Svaluto-Ferro, 2021. "Infinite-dimensional polynomial processes," Finance and Stochastics, Springer, vol. 25(2), pages 383-426, April.
    4. Christa Cuchiero, 2017. "Polynomial processes in stochastic portfolio theory," Papers 1705.03647, arXiv.org.
    5. Cuchiero, Christa, 2019. "Polynomial processes in stochastic portfolio theory," Stochastic Processes and their Applications, Elsevier, vol. 129(5), pages 1829-1872.
    6. Francesca Biagini & Yinglin Zhang, 2017. "Reduced-form framework under model uncertainty," Papers 1707.04475, arXiv.org, revised Mar 2018.
    7. Filipović, Damir & Larsson, Martin & Pulido, Sergio, 2020. "Markov cubature rules for polynomial processes," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 1947-1971.
    8. Damir Filipovi'c & Martin Larsson & Sergio Pulido, 2017. "Markov cubature rules for polynomial processes," Papers 1707.06849, arXiv.org, revised Jun 2019.
    9. Christa Cuchiero & Francesco Guida & Luca di Persio & Sara Svaluto-Ferro, 2021. "Measure-valued affine and polynomial diffusions," Papers 2112.15129, arXiv.org.
    10. Christa Cuchiero & Sara Svaluto-Ferro, 2019. "Infinite dimensional polynomial processes," Papers 1911.02614, arXiv.org.

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    More about this item

    Keywords

    Life insurance liability; Polynomial diffusion; Benchmark approach; Stochastic mortality intensity; Benchmarked risk-minimization;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G19 - Financial Economics - - General Financial Markets - - - Other

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