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Reserve-dependent benefits and costs in life and health insurance contracts

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  • Christiansen, Marcus
  • Denuit, Michel
  • Dhaene, Jan

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.
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Suggested Citation

  • Christiansen, Marcus & Denuit, Michel & Dhaene, Jan, 2014. "Reserve-dependent benefits and costs in life and health insurance contracts," LIDAM Reprints ISBA 2014017, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvar:2014017
    Note: In : Insurance: Mathematics and Economics, vol. 57, p. 132-137 (2014)
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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. Stephen Fier & Andre Liebenberg, 2013. "Life Insurance Lapse Behavior," North American Actuarial Journal, Taylor & Francis Journals, vol. 17(2), pages 153-167.
    3. 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.
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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. 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.
    3. 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.
    4. David Bogataj & Marija Bogataj & Samo Drobne, 2022. "Long-Term Care Sustainable Networks in ADRION Region," Sustainability, MDPI, vol. 14(18), pages 1-23, September.
    5. 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.

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    JEL classification:

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

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