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A review of the Markov model of life insurance with a view to surplus

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

Abstract

We review Markov models of surplus in life insurance based on a counting process following Norberg (1991), uniting probabilistic theory with elements of practice largely drawn from UK experience. First, we organize models systematically based on one and two technical bases, including a suitable descriptive notation. Extending this to three technical bases to accommodate different valuation approaches leads us: (a) to expand the definition of 'technical basis' to include non-contractual cashflows recognized in the associated Thiele equation; and (b) to add new (mainly) systematic terms to the surplus. Making these cashflows dynamic or 'quasi-contractual' covers many real applications, and we give two as examples, the paid-up valuation principle and reversionary bonus on participating contracts.

Suggested Citation

  • Oytun Hac{c}ar{i}z & Torsten Kleinow & Angus S. Macdonald, 2025. "A review of the Markov model of life insurance with a view to surplus," Papers 2509.00011, arXiv.org.
    • Handle: RePEc:arx:papers:2509.00011
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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. Marcus C. Christiansen & Michel M. Denuit & Jan Dhaene, 2014. "Reserve-Dependent Benefits and Costs in Life and Health Insurance Contracts," Tinbergen Institute Discussion Papers 14-117/IV/DSF80, Tinbergen Institute.
    4. Møller,Thomas & Steffensen,Mogens, 2007. "Market-Valuation Methods in Life and Pension Insurance," Cambridge Books, Cambridge University Press, number 9780521868778, Enero-Abr.
    5. Craig Turnbull, 2017. "A History of British Actuarial Thought," Springer Books, Springer, number 978-3-319-33183-6, January.
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