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Cash flows and policyholder behaviour in the semi-Markov life insurance setup

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  • Kristian Buchardt
  • Thomas Møller
  • Kristian Bjerre Schmidt

Abstract

Within the setup of a semi-Markov process in a finite state space, we consider a life insurance contract. First, without the modelling of policyholder behaviour, we show how to calculate the expected cash flow associated with future payments, and to that end we present a version of Kolmogorov’s forward integro-differential equation. The semi-Markov model is then extended to include modelling of surrender and free policy behaviour, and the main result is a modification of Kolmogorov’s forward integro-differential equation, such that the cash flow can be calculated without significantly more complexity than the cash flow without policyholder modelling. The result is also demonstrated for the traditional Markov case where there is no duration dependence, and numerical examples are studied.

Suggested Citation

  • Kristian Buchardt & Thomas Møller & Kristian Bjerre Schmidt, 2015. "Cash flows and policyholder behaviour in the semi-Markov life insurance setup," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2015(8), pages 660-688, November.
    • Handle: RePEc:taf:sactxx:v:2015:y:2015:i:8:p:660-688
    DOI: 10.1080/03461238.2013.879919
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    Cited by:

    1. Ahmad, Jamaal & Bladt, Mogens & Furrer, Christian, 2023. "Aggregate Markov models in life insurance: Properties and valuation," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 50-69.
    2. Mathias Valla & Xavier Milhaud & Anani Ayodélé Olympio, 2023. "Including individual Customer Lifetime Value and competing risks in tree-based lapse management strategies," Post-Print hal-03903047, HAL.
    3. Oliver Lunding Sandqvist, 2023. "A multistate approach to disability insurance reserving with information delays," Papers 2312.14324, arXiv.org.

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