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Dynamics of state-wise prospective reserves in the presence of non-monotone information

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  • Christiansen, Marcus C.
  • Furrer, Christian

Abstract

In the presence of monotone information, the stochastic Thiele equation describing the dynamics of state-wise prospective reserves is closely related to the classic martingale representation theorem. When the information utilized by the insurer is non-monotone, the classic martingale theory does not apply. By taking an infinitesimal approach, we derive a generalized stochastic Thiele equation that allows for information discarding. En passant, we solve some open problems for the classic case of monotone information. The results and their implication in practice are illustrated via examples where information is discarded upon and after stochastic retirement.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:97:y:2021:i:c:p:81-98
    DOI: 10.1016/j.insmatheco.2021.01.005
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    References listed on IDEAS

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    1. Linnemann, Per, 1993. "On the application of Thiele's differential equation in life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 13(1), pages 63-74, September.
    2. Ramlau-Hansen, Henrik, 1988. "The emergence of profit in life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 7(4), pages 225-236, December.
    3. Christiansen, Marcus C., 2008. "A sensitivity analysis concept for life insurance with respect to a valuation basis of infinite dimension," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 680-690, April.
    4. 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.
    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. Ragnar Norberg, 1999. "A theory of bonus in life insurance," Finance and Stochastics, Springer, vol. 3(4), pages 373-390.
    7. Steffensen, Mogens, 2000. "A no arbitrage approach to Thiele's differential equation," Insurance: Mathematics and Economics, Elsevier, vol. 27(2), pages 201-214, October.
    8. Christiansen, Marcus C. & Steffensen, Mogens, 2013. "Safe-Side Scenarios For Financial And Biometrical Risk," ASTIN Bulletin, Cambridge University Press, vol. 43(3), pages 323-357, September.
    9. Marcus C. Christiansen, 2018. "A martingale concept for non-monotone information in a jump process framework," Papers 1811.00952, arXiv.org, revised Jan 2021.
    10. Christiansen, Marcus C., 2008. "A sensitivity analysis of typical life insurance contracts with respect to the technical basis," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 787-796, April.
    11. 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.
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    Citations

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    Cited by:

    1. Kristian Buchardt & Christian Furrer & Oliver Lunding Sandqvist, 2022. "Transaction time models in multi-state life insurance," Papers 2209.06902, arXiv.org, revised Feb 2023.
    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.
    3. Nießl, Alexandra & Allignol, Arthur & Beyersmann, Jan & Mueller, Carina, 2023. "Statistical inference for state occupation and transition probabilities in non-Markov multi-state models subject to both random left-truncation and right-censoring," Econometrics and Statistics, Elsevier, vol. 25(C), pages 110-124.
    4. Oliver Lunding Sandqvist, 2023. "A multistate approach to disability insurance reserving with information delays," Papers 2312.14324, arXiv.org.

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    More about this item

    Keywords

    Life insurance; Stochastic Thiele equations; Infinitesimal martingales; Marked point processes; Stochastic retirement;
    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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