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Reserve-Dependent Benefits and Costs in Life and Health Insurance Contracts

Author

Listed:
  • Marcus C. Christiansen

    (University of Ulm, Germany)

  • Michel M. Denuit

    (Université Catholique de Louvain, Belgium)

  • Jan Dhaene

    (Katholieke Universiteit Leuven, Belgium, University of the Free State, South Africa)

Abstract

Premiums and benefits associated with traditional life insurance contracts are usually specified as fixed amounts in policy conditions. However, reserve-dependent surrender values and reserve-dependent expenses are common in insurance practice. The famous Cantelli theorem in life insurance ensures that under appropriate assumptions surrendering can be ignored in reserve calculations provided the surrender payment equals the accumulated reserve. In this paper, more complex reserve-dependent payment patterns are considered, in line with insurance practice. Explicit formulas are derived for the corresponding reserve.

Suggested Citation

  • Marcus C. Christiansen & Michel M. Denuit & Jan Dhaene, 2014. "Reserve-Dependent Benefits and Costs in Life and Health Insurance Contracts," Tinbergen Institute Discussion Papers 14-117/IV/DSF80, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20140117
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    File URL: https://papers.tinbergen.nl/14117.pdf
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    References listed on IDEAS

    as
    1. Wolthuis, Henk & Hoem, Jan M., 1990. "The retrospective premium reserve," Insurance: Mathematics and Economics, Elsevier, vol. 9(2-3), pages 229-234, September.
    2. Milbrodt, Hartmut & Stracke, Andrea, 1997. "Markov models and Thiele's integral equations for the prospective reserve," Insurance: Mathematics and Economics, Elsevier, vol. 19(3), pages 187-235, May.
    3. Stephen Fier & Andre Liebenberg, 2013. "Life Insurance Lapse Behavior," North American Actuarial Journal, Taylor & Francis Journals, vol. 17(2), pages 153-167.
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    Citations

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    Cited by:

    1. 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.
    2. Kabuche, Doreen & Sherris, Michael & Villegas, Andrés M. & Ziveyi, Jonathan, 2024. "Pooling functional disability and mortality in long-term care insurance and care annuities: A matrix approach for multi-state pools," Insurance: Mathematics and Economics, Elsevier, vol. 116(C), pages 165-188.
    3. Marcus C. Christiansen & Christian Furrer, 2024. "Canonical insurance models: stochastic equations and comparison theorems," Papers 2411.12522, arXiv.org.
    4. Dacev, Nikola, 2017. "The Necessity Of Legal Arrangement Of Unit-Linked Life Insurance Products," UTMS Journal of Economics, University of Tourism and Management, Skopje, Macedonia, vol. 8(3), pages 259-269.
    5. Djehiche, Boualem & Löfdahl, Björn, 2016. "Nonlinear reserving in life insurance: Aggregation and mean-field approximation," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 1-13.
    6. David Bogataj & Marija Bogataj & Samo Drobne, 2022. "Long-Term Care Sustainable Networks in ADRION Region," Sustainability, MDPI, vol. 14(18), pages 1-23, September.

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    More about this item

    Keywords

    life insurance; multistate models; Markov process; surrender value; Cantelli theorem;
    All these keywords.

    JEL classification:

    • G00 - Financial Economics - - General - - - General

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