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Biometric worst-case scenarios for multi-state life insurance policies

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  • Christiansen, Marcus C.

Abstract

It is common actuarial practice to calculate premiums and reserves under a set of biometric assumptions that represent a worst-case scenario for the insurer. The new solvency regime of the European Union (Solvency II) also uses worst-case scenarios for the calculation of solvency capital requirements for life insurance business. Surprisingly, the actuarial literature so far offers no exact method for the construction of biometric scenarios that let premiums and reserves be always on the safe side with respect to a given confidence band for the biometric second-order basis. The present paper partly fills this gap by introducing a general method that allows one to construct such scenarios for homogenous portfolios of life insurance policies. The results are especially informative for life insurance policies with mixed character (e.g. survival and occurrence character). Two examples are given that illustrate the new method, demonstrate its usefulness for the calculation of premiums and reserves, and show how the new approach could improve the calculation of biometric solvency reserves for Solvency II.

Suggested Citation

  • Christiansen, Marcus C., 2010. "Biometric worst-case scenarios for multi-state life insurance policies," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 190-197, October.
    • Handle: RePEc:eee:insuma:v:47:y:2010:i:2:p:190-197
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    References listed on IDEAS

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    1. Ramlau-Hansen, Henrik, 1988. "The emergence of profit in life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 7(4), pages 225-236, December.
    2. Christiansen, Marcus C., 2008. "A sensitivity analysis concept for life insurance with respect to a valuation basis of infinite dimension," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 680-690, April.
    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.
    4. Christiansen, Marcus C., 2008. "A sensitivity analysis of typical life insurance contracts with respect to the technical basis," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 787-796, April.
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    Cited by:

    1. Marcus Christiansen, 2012. "Multistate models in health insurance," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 96(2), pages 155-186, June.
    2. Christiansen, Marcus C. & Denuit, Michel M., 2013. "Worst-case actuarial calculations consistent with single- and multiple-decrement life tables," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 1-5.
    3. Christiansen, Marcus & Denuit, Michel, 2012. "Worst-case actuarial calculations consistent with single- and multiple-decrement life tables," LIDAM Discussion Papers ISBA 2012027, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Theis Bathke & Marcus Christiansen, 2022. "Two-dimensional forward and backward transition rates," Papers 2204.12766, arXiv.org.

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