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Nonlinear reserving and multiple contract modifications in life insurance

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  • Christiansen, Marcus C.
  • Djehiche, Boualem

Abstract

Life insurance cash flows become reserve dependent when contract conditions are modified during the contract term on condition that actuarial equivalence is maintained. As a result, insurance cash flows and prospective reserves depend on each other in a circular way, and it is a non-trivial problem to solve that circularity and make cash flows and prospective reserves well-defined. In Markovian models, the (stochastic) Thiele equation and the Cantelli Theorem are the standard tools for solving the circularity issue and for maintaining actuarial equivalence. This paper expands the stochastic Thiele equation and the Cantelli Theorem to non-Markovian frameworks and presents a recursive scheme for the calculation of multiple contract modifications.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:93:y:2020:i:c:p:187-195
    DOI: 10.1016/j.insmatheco.2020.05.004
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    References listed on IDEAS

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    1. 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.
    2. Ragnar Norberg, 2005. "Anomalous PDEs in Markov chains: Domains of validity and numerical solutions," Finance and Stochastics, Springer, vol. 9(4), pages 519-537, October.
    3. Djehiche, Boualem & Löfdahl, Björn, 2016. "Nonlinear reserving in life insurance: Aggregation and mean-field approximation," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 1-13.
    4. Marcus Christiansen, 2012. "Multistate models in health insurance," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 96(2), pages 155-186, June.
    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. Møller,Thomas & Steffensen,Mogens, 2007. "Market-Valuation Methods in Life and Pension Insurance," Cambridge Books, Cambridge University Press, number 9780521868778, May.
    7. Kristian Buchardt & Thomas Møller, 2015. "Life Insurance Cash Flows with Policyholder Behavior," Risks, MDPI, vol. 3(3), pages 1-28, July.
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    Cited by:

    1. 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.
    2. Marcus C. Christiansen & Christian Furrer, 2024. "Canonical insurance models: stochastic equations and comparison theorems," Papers 2411.12522, arXiv.org.
    3. Debbie Kusch Falden & Anna Kamille Nyegaard, 2021. "Retrospective Reserves and Bonus with Policyholder Behavior," Risks, MDPI, vol. 9(1), pages 1-28, January.
    4. Marcus C. Christiansen & Christian Furrer, 2020. "Dynamics of state-wise prospective reserves in the presence of non-monotone information," Papers 2003.02173, arXiv.org, revised Jan 2021.
    5. 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.
    6. Marcus C. Christiansen, 2021. "Time-dynamic evaluations under non-monotone information generated by marked point processes," Finance and Stochastics, Springer, vol. 25(3), pages 563-596, July.
    7. Christiansen, Marcus C. & Furrer, Christian, 2021. "Dynamics of state-wise prospective reserves in the presence of non-monotone information," Insurance: Mathematics and Economics, Elsevier, vol. 97(C), pages 81-98.

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