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Dependent interest and transition rates in life insurance

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  • Buchardt, Kristian

Abstract

For market consistent life insurance liabilities modelled with a multi-state Markov chain, it is of importance to consider the interest and transition rates as stochastic processes, for example in order to consider hedging possibilities of the risks, and for risk measurement. In the literature, this is usually done with an assumption of independence between the interest and transition rates. In this paper, it is shown how to valuate life insurance liabilities using affine processes for modelling dependent interest and transition rates. This approach leads to the introduction of so-called dependent forward rates. We propose a specific model for surrender modelling, and within this model the dependent forward rates are calculated, and the market value and the Solvency II capital requirement are examined for a simple savings contract.

Suggested Citation

  • Buchardt, Kristian, 2014. "Dependent interest and transition rates in life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 167-179.
    • Handle: RePEc:eee:insuma:v:55:y:2014:i:c:p:167-179
    DOI: 10.1016/j.insmatheco.2014.01.004
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    References listed on IDEAS

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    Cited by:

    1. Jiwook Jang & Siti Norafidah Mohd Ramli, 2018. "Hierarchical Markov Model in Life Insurance and Social Benefit Schemes," Risks, MDPI, vol. 6(3), pages 1-17, June.
    2. Marcus Christiansen & Andreas Niemeyer, 2015. "On the forward rate concept in multi-state life insurance," Finance and Stochastics, Springer, vol. 19(2), pages 295-327, April.
    3. Mathias Valla & Xavier Milhaud & Anani Ayodélé Olympio, 2023. "Including individual Customer Lifetime Value and competing risks in tree-based lapse management strategies," Post-Print hal-03903047, HAL.
    4. Berdin, Elia & Gründl, Helmut & Kubitza, Christian, 2017. "Rising interest rates, lapse risk, and the stability of life insurers," ICIR Working Paper Series 29/17, Goethe University Frankfurt, International Center for Insurance Regulation (ICIR).
    5. Xavier Milhaud & Christophe Dutang, 2018. "Lapse tables for lapse risk management in insurance: a competing risk approach," Post-Print hal-01727669, HAL.
    6. Jamaal Ahmad & Mogens Bladt, 2022. "Phase-type representations of stochastic interest rates with applications to life insurance," Papers 2207.11292, arXiv.org, revised Nov 2022.
    7. Mathias Valla & Xavier Milhaud & Anani Ayodélé Olympio, 2023. "Including individual Customer Lifetime Value and competing risks in tree-based lapse management strategy," Working Papers hal-03903047, HAL.
    8. Kristian Buchardt & Christian Furrer & Mogens Steffensen, 2019. "Forward transition rates," Finance and Stochastics, Springer, vol. 23(4), pages 975-999, October.
    9. Kristian Buchardt & Thomas Møller, 2015. "Life Insurance Cash Flows with Policyholder Behavior," Risks, MDPI, vol. 3(3), pages 1-28, July.
    10. Xavier Milhaud & Christophe Dutang, 2018. "Lapse tables for lapse risk management in insurance: a competing risk approach," Post-Print hal-01985256, HAL.
    11. K. Buchardt & C. Furrer & M. Steffensen, 2018. "Forward transition rates," Papers 1811.00137, arXiv.org, revised Apr 2019.
    12. Jang, Jiwook & Mohd Ramli, Siti Norafidah, 2015. "Jump diffusion transition intensities in life insurance and disability annuity," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 440-451.

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    More about this item

    Keywords

    Affine processes; Doubly stochastic process; Multi-state life insurance models; Policyholder behaviour; Solvency II; Surrender;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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