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Retrospective Reserves and Bonus with Policyholder Behavior

Author

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  • Debbie Kusch Falden

    (Department of Mathematical Science (MATH), University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark
    These authors contributed equally to this work.)

  • Anna Kamille Nyegaard

    (Department of Mathematical Science (MATH), University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark
    These authors contributed equally to this work.)

Abstract

Legislation imposes insurance companies to project their assets and liabilities in various financial scenarios. Within the setup of with-profit life insurance, we consider retrospective reserves and bonus, and we study projection of balances with and without policyholder behavior. The projection resides in a system of differential equations of the savings account and the surplus, and the policyholder behavior options surrender and conversion to free-policy are included. The inclusion results in a structure where the system of differential equations of the savings account and the surplus is non-trivial. We consider a case where we are able to find accurate differential equations and suggest an approximation method to project the savings account and the surplus, including policyholder behavior, in general. To highlight the practical applications of the results in this paper, we study a numerical example.

Suggested Citation

  • Debbie Kusch Falden & Anna Kamille Nyegaard, 2021. "Retrospective Reserves and Bonus with Policyholder Behavior," Risks, MDPI, vol. 9(1), pages 1-28, January.
    • Handle: RePEc:gam:jrisks:v:9:y:2021:i:1:p:15-:d:475059
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    References listed on IDEAS

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    Cited by:

    1. Florian Gach & Simon Hochgerner & Eva Kienbacher & Gabriel Schachinger, 2023. "Mean-field Libor market model and valuation of long term guarantees," Papers 2310.09022, arXiv.org, revised Nov 2023.
    2. Corina Constantinescu & Julia Eisenberg, 2021. "Special Issue “Interplay between Financial and Actuarial Mathematics”," Risks, MDPI, vol. 9(8), pages 1-3, July.
    3. Anna Kamille Nyegaard & Johan Raunkjær Ott & Mogens Steffensen, 2021. "An Intrinsic Value Approach to Valuation with Forward–Backward Loops in Dividend Paying Stocks," Mathematics, MDPI, vol. 9(13), pages 1-23, June.

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