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Life Insurance Cash Flows with Policyholder Behavior

Author

Listed:
  • Kristian Buchardt

    (PFA Pension, Sundkrogsgade 4, DK-2100 Copenhagen Ø, Denmark
    Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen Ø, Denmark)

  • Thomas Møller

    (PFA Pension, Sundkrogsgade 4, DK-2100 Copenhagen Ø, Denmark
    Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen Ø, Denmark)

Abstract

The problem of the valuation of life insurance payments with policyholder behavior is studied. First, a simple survival model is considered, and it is shown how cash flows without policyholder behavior can be modified to include surrender and free policy behavior by calculation of simple integrals. In the second part, a more general disability model with recovery is studied. Here, cash flows are determined by solving a modified Kolmogorov forward differential equation. We conclude the paper with numerical examples illustrating the methods proposed and the impact of policyholder behavior.

Suggested Citation

  • Kristian Buchardt & Thomas Møller, 2015. "Life Insurance Cash Flows with Policyholder Behavior," Risks, MDPI, vol. 3(3), pages 1-28, July.
    • Handle: RePEc:gam:jrisks:v:3:y:2015:i:3:p:290-317:d:53175
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    References listed on IDEAS

    as
    1. Buchardt, Kristian, 2014. "Dependent interest and transition rates in life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 167-179.
    2. Møller,Thomas & Steffensen,Mogens, 2007. "Market-Valuation Methods in Life and Pension Insurance," Cambridge Books, Cambridge University Press, number 9780521868778, October.
    3. Steffensen, Mogens, 2002. "Intervention options in life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 71-85, August.
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    Citations

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    Cited by:

    1. Ahmad, Jamaal & Bladt, Mogens & Furrer, Christian, 2023. "Aggregate Markov models in life insurance: Properties and valuation," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 50-69.
    2. 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.
    3. Christiansen, Marcus C. & Furrer, Christian, 2022. "Extension of as-if-Markov modeling to scaled payments," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 288-306.
    4. Christiansen, Marcus C. & Djehiche, Boualem, 2020. "Nonlinear reserving and multiple contract modifications in life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 187-195.
    5. Kristian Buchardt & Christian Furrer & Mogens Steffensen, 2019. "Forward transition rates," Finance and Stochastics, Springer, vol. 23(4), pages 975-999, October.
    6. Jamaal Ahmad, 2021. "Multivariate higher order moments in multi-state life insurance," Papers 2102.11714, arXiv.org, revised Oct 2021.
    7. Christian Furrer, 2022. "Scaled insurance cash flows: representation and computation via change of measure techniques," Finance and Stochastics, Springer, vol. 26(2), pages 359-382, April.

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