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Scaled insurance cash flows: representation and computation via change of measure techniques

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  • Christian Furrer

    (University of Copenhagen)

Abstract

We consider general multi-state life insurance payment processes and study the expected accumulated cash flows that arise when modifying the payments by scaling factors depending on the time of occurrence of specific events. Such modified payment processes arise naturally in the context of incidental policyholder behaviour. We associate to the modifications new probability measures which allow a standard representation of the expected accumulated cash flows. The measures are characterised in terms of the original measure and the scaling factors. Examples for Markov chains illuminate the relevance of our concepts and results to actuarial practice.

Suggested Citation

  • Christian Furrer, 2022. "Scaled insurance cash flows: representation and computation via change of measure techniques," Finance and Stochastics, Springer, vol. 26(2), pages 359-382, April.
    • Handle: RePEc:spr:finsto:v:26:y:2022:i:2:d:10.1007_s00780-022-00472-z
    DOI: 10.1007/s00780-022-00472-z
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    References listed on IDEAS

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    1. Kardaras, Constantinos & Kreher, Dörte & Nikeghbali, Ashkan, 2015. "Strict local martingales and bubbles," LSE Research Online Documents on Economics 64967, London School of Economics and Political Science, LSE Library.
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    3. Christiansen, Marcus C. & Djehiche, Boualem, 2020. "Nonlinear reserving and multiple contract modifications in life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 187-195.
    4. Kristian Buchardt & Christian Furrer & Mogens Steffensen, 2019. "Forward transition rates," Finance and Stochastics, Springer, vol. 23(4), pages 975-999, October.
    5. Milbrodt, Hartmut & Stracke, Andrea, 1997. "Markov models and Thiele's integral equations for the prospective reserve," Insurance: Mathematics and Economics, Elsevier, vol. 19(3), pages 187-235, May.
    6. Kristian Buchardt & Thomas Møller, 2015. "Life Insurance Cash Flows with Policyholder Behavior," Risks, MDPI, vol. 3(3), pages 1-28, July.
    7. K. Buchardt & C. Furrer & M. Steffensen, 2018. "Forward transition rates," Papers 1811.00137, arXiv.org, revised Apr 2019.
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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. Christiansen, Marcus C. & Furrer, Christian, 2022. "Extension of as-if-Markov modeling to scaled payments," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 288-306.

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    More about this item

    Keywords

    Multi-state life insurance; Incidental policyholder behaviour; Jump processes; Föllmer measures;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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