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A theory of bonus in life insurance

Author

Listed:
  • Ragnar Norberg

    (Laboratory of Actuarial Mathematics, Universitetsparken 5, DK-2100 Copenhagen û, Denmark)

Abstract

The issue of bonus in life insurance is considered in a model framework where the traditional set-up is extended by letting the experience basis (mortality, interest, etc.) be stochastic. A novel definition of the technical surplus on an insurance contract is proposed, and basic principles for its repayment as bonus are discussed. Making the experience basis an endogenous part of the model opens possibilities of model-based prognostication of future bonuses. Numerical illustrations are provided.

Suggested Citation

  • Ragnar Norberg, 1999. "A theory of bonus in life insurance," Finance and Stochastics, Springer, vol. 3(4), pages 373-390.
    • Handle: RePEc:spr:finsto:v:3:y:1999:i:4:p:373-390
    Note: received: January 1998; final version received: September 1998
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    Citations

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    Cited by:

    1. Ninna Reitzel Jensen & Kristian Juul Schomacker, 2015. "A Two-Account Life Insurance Model for Scenario-Based Valuation Including Event Risk," Risks, MDPI, vol. 3(2), pages 1-36, June.
    2. Dahl, Mikkel, 2004. "Stochastic mortality in life insurance: market reserves and mortality-linked insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 35(1), pages 113-136, August.
    3. Kallestrup-Lamb, Malene & Søgaard Laursen, Nicolai, 2024. "Longevity hedge effectiveness using socioeconomic indices," Insurance: Mathematics and Economics, Elsevier, vol. 114(C), pages 242-251.
    4. Møller, T., 2002. "On Valuation and Risk Management at the Interface of Insurance and Finance," British Actuarial Journal, Cambridge University Press, vol. 8(4), pages 787-827, October.
    5. Andreas Niemeyer, 2015. "Safety Margins for Systematic Biometric and Financial Risk in a Semi-Markov Life Insurance Framework," Risks, MDPI, vol. 3(1), pages 1-26, January.
    6. Jarner, Søren Fiig & Kronborg, Morten Tolver, 2016. "Entrance times of random walks: With applications to pension fund modeling," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 1-20.
    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.
    8. Thomas Møller, 2001. "Risk-minimizing hedging strategies for insurance payment processes," Finance and Stochastics, Springer, vol. 5(4), pages 419-446.
    9. Buchardt, Kristian, 2014. "Dependent interest and transition rates in life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 167-179.
    10. Asmussen, Soren & Moller, Jakob R., 2003. "Risk comparisons of premium rules: optimality and a life insurance study," Insurance: Mathematics and Economics, Elsevier, vol. 32(3), pages 331-344, July.
    11. Oytun Hac{c}ar{i}z & Torsten Kleinow & Angus S. Macdonald, 2023. "On Technical Bases and Surplus in Life Insurance," Papers 2310.16927, arXiv.org.
    12. 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.
    13. Julian Jetses & Marcus C. Christiansen, 2021. "A General Surplus Decomposition Principle in Life Insurance," Papers 2111.12967, arXiv.org.
    14. Jamaal Ahmad & Kristian Buchardt & Christian Furrer, 2020. "Computation of bonus in multi-state life insurance," Papers 2007.04051, arXiv.org, revised Nov 2023.
    15. Debbie Kusch Falden & Anna Kamille Nyegaard, 2021. "Retrospective Reserves and Bonus with Policyholder Behavior," Risks, MDPI, vol. 9(1), pages 1-28, January.
    16. 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.
    17. Tenorio Villal¢n, Angel F. & Martín Caraballo, Ana M. & Paralera Morales, Concepción & Contreras Rubio, Ignacio, 2013. "Ecuaciones diferenciales y en diferencias aplicadas a los conceptos económicos y financieros || Differential and Difference Equations Applied to Economic and Financial Concepts," Revista de Métodos Cuantitativos para la Economía y la Empresa = Journal of Quantitative Methods for Economics and Business Administration, Universidad Pablo de Olavide, Department of Quantitative Methods for Economics and Business Administration, vol. 16(1), pages 165-199, December.
    18. Ragnar Norberg, 2013. "Optimal hedging of demographic risk in life insurance," Finance and Stochastics, Springer, vol. 17(1), pages 197-222, January.
    19. Francesca Biagini & Andreas Groll & Jan Widenmann, 2016. "Risk Minimization for Insurance Products via F-Doubly Stochastic Markov Chains," Risks, MDPI, vol. 4(3), pages 1-26, July.

    More about this item

    Keywords

    Safety margins; prospective reserves; retrospective reserves; stochastic interest; stochastic mortality; counting processes;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • G23 - Financial Economics - - Financial Institutions and Services - - - Non-bank Financial Institutions; Financial Instruments; Institutional Investors

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