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On Technical Bases and Surplus in Life Insurance

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  • Oytun Hac{c}ar{i}z
  • Torsten Kleinow
  • Angus S. Macdonald

Abstract

We revisit surplus on general life insurance contracts, represented by Markov models. We classify technical bases in terms of boundary conditions in Thiele's equation(s), allowing more general regulations than Scandinavian-style `first-order/second-order' regimes, and replacing the traditional retrospective policy value. We propose a `canonical' model with three technical bases (premium, valuation, accumulation) and show how each pair of bases defines premium loadings and surplus. Along with a `true' or `real-world' experience basis, this expands fundamental results of Ramlau-Hansen (1988a). We conclude with two applications: lapse-supported business; and the retrospectively-oriented regime proposed by M{\o}ller & Steffensen (2007).

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  • 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.
    • Handle: RePEc:arx:papers:2310.16927
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    References listed on IDEAS

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    1. 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.
    2. P. Linnemann, 2003. "An Actuarial Analysis of Participating Life Insurance," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2003(2), pages 153-176.
    3. Møller,Thomas & Steffensen,Mogens, 2007. "Market-Valuation Methods in Life and Pension Insurance," Cambridge Books, Cambridge University Press, number 9780521868778, October.
    4. Craig Turnbull, 2017. "A History of British Actuarial Thought," Springer Books, Springer, number 978-3-319-33183-6, January.
    5. Ragnar Norberg, 1999. "A theory of bonus in life insurance," Finance and Stochastics, Springer, vol. 3(4), pages 373-390.
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