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A General Surplus Decomposition Principle in Life Insurance

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  • Julian Jetses
  • Marcus C. Christiansen

Abstract

In with-profit life insurance, the prudent valuation of future insurance liabilities leads to systematic surplus that mainly belongs to the policyholders and is redistributed as bonus. For a fair and lawful redistribution of surplus the insurer needs to decompose the total portfolio surplus with respect to the contributions of individual policies and with respect to different risk sources. For this task, actuaries have a number of heuristic decomposition formulas, but an overarching decomposition principle is still missing. This paper fills that gap by introducing a so-called ISU decomposition principle that bases on infinitesimal sequential updates of the insurer's valuation basis. It is shown that the existing heuristic decomposition formulas can be replicated as ISU decompositions. Furthermore, alternative decomposition principles and their relation to the ISU decomposition principle are discussed. The generality of the ISU concept makes it a useful tool also beyond classical surplus decompositions in life insurance.

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  • Julian Jetses & Marcus C. Christiansen, 2021. "A General Surplus Decomposition Principle in Life Insurance," Papers 2111.12967, arXiv.org.
    • Handle: RePEc:arx:papers:2111.12967
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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. Ragnar Norberg, 1999. "A theory of bonus in life insurance," Finance and Stochastics, Springer, vol. 3(4), pages 373-390.
    3. Fortin, Nicole & Lemieux, Thomas & Firpo, Sergio, 2011. "Decomposition Methods in Economics," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 4, chapter 1, pages 1-102, Elsevier.
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    5. Martin Biewen, 2014. "A general decomposition formula with interaction effects," Applied Economics Letters, Taylor & Francis Journals, vol. 21(9), pages 636-642, June.
    6. Ramlau-Hansen, Henrik, 1991. "Distribution of Surplus in Life Insurance," ASTIN Bulletin, Cambridge University Press, vol. 21(1), pages 57-71, April.
    7. Møller,Thomas & Steffensen,Mogens, 2007. "Market-Valuation Methods in Life and Pension Insurance," Cambridge Books, Cambridge University Press, number 9780521868778, September.
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