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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.

Suggested Citation

  • Julian Jetses & Marcus C. Christiansen, 2022. "A general surplus decomposition principle in life insurance," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2022(10), pages 901-925, November.
  • Handle: RePEc:taf:sactxx:v:2022:y:2022:i:10:p:901-925
    DOI: 10.1080/03461238.2022.2049636
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    Cited by:

    1. Oytun Hac{c}ar{i}z & Torsten Kleinow & Angus S. Macdonald, 2023. "On Technical Bases and Surplus in Life Insurance," Papers 2310.16927, arXiv.org.
    2. Solveig Flaig & Gero Junike, 2023. "Profit and loss attribution: An empirical study," Papers 2309.07667, arXiv.org, revised Dec 2023.

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