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The effect of policyholders' rationality on unit-linked life insurance contracts with surrender guarantees

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  • Jing Li
  • Alexander Szimayer

Abstract

We study the valuation of unit-linked life insurance contracts with surrender guarantees. Instead of solving an optimal stopping problem, we propose a more realistic approach accounting for policyholders' rationality in exercising their surrender option. The valuation is conducted at the portfolio level by assuming that the surrender rate of the representative agent is bounded from below and from above. The lower bound corresponds to purely exogenous surrender, and the difference between the upper bound and the lower bound represents the rationality of the policyholders. The valuation problem is formulated by a PDE approach and solved with the finite difference method. We show that the rationality of the policyholders has a significant effect on average contract value and hence on the fair contract design. We also present the separating boundary between purely exogenous surrender and endogenous surrender. This provides implications on the predicted surrender activity of the policyholders.

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  • Jing Li & Alexander Szimayer, 2014. "The effect of policyholders' rationality on unit-linked life insurance contracts with surrender guarantees," Quantitative Finance, Taylor & Francis Journals, vol. 14(2), pages 327-342, February.
    • Handle: RePEc:taf:quantf:v:14:y:2014:i:2:p:327-342
    DOI: 10.1080/14697688.2013.825922
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    Cited by:

    1. Anne MacKay & Maciej Augustyniak & Carole Bernard & Mary R. Hardy, 2017. "Risk Management of Policyholder Behavior in Equity-Linked Life Insurance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(2), pages 661-690, June.
    2. Cheng, Chunli, 2022. "Beyond death: The impact of a population-wide health shock on life insurance," The North American Journal of Economics and Finance, Elsevier, vol. 63(C).
    3. Cheng, Chunli & Hilpert, Christian & Miri Lavasani, Aidin & Schaefer, Mick, 2023. "Surrender contagion in life insurance," European Journal of Operational Research, Elsevier, vol. 305(3), pages 1465-1479.
    4. Cheng, Chunli & Li, Jing, 2018. "Early default risk and surrender risk: Impacts on participating life insurance policies," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 30-43.
    5. Christian Hilpert, 2020. "The Effect of Risk Aversion and Loss Aversion on Equity‐Linked Life Insurance With Surrender Guarantees," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 87(3), pages 665-687, September.
    6. Belssing Taruvinga, 2019. "Solving Selected Problems on American Option Pricing with the Method of Lines," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 4-2019.

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