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Stochastic Claims Reserving Methods with State Space Representations: A Review

Author

Listed:
  • Nataliya Chukhrova

    (Faculty of Business Administration, University of Hamburg, 20146 Hamburg, Germany)

  • Arne Johannssen

    (Faculty of Business Administration, University of Hamburg, 20146 Hamburg, Germany)

Abstract

Often, the claims reserves exceed the available equity of non-life insurance companies and a change in the claims reserves by a small percentage has a large impact on the annual accounts. Therefore, it is of vital importance for any non-life insurer to handle claims reserving appropriately. Although claims data are time series data, the majority of the proposed (stochastic) claims reserving methods is not based on time series models. Among the time series models, state space models combined with Kalman filter learning algorithms have proven to be very advantageous as they provide high flexibility in modeling and an accurate detection of the temporal dynamics of a system. Against this backdrop, this paper aims to provide a comprehensive review of stochastic claims reserving methods that have been developed and analyzed in the context of state space representations. For this purpose, relevant articles are collected and categorized, and the contents are explained in detail and subjected to a conceptual comparison.

Suggested Citation

  • Nataliya Chukhrova & Arne Johannssen, 2021. "Stochastic Claims Reserving Methods with State Space Representations: A Review," Risks, MDPI, vol. 9(11), pages 1-55, November.
    • Handle: RePEc:gam:jrisks:v:9:y:2021:i:11:p:198-:d:672160
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    References listed on IDEAS

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    1. Piet de Jong, 2006. "Forecasting Runoff Triangles," North American Actuarial Journal, Taylor & Francis Journals, vol. 10(2), pages 28-38.
    2. Verrall, R.J., 1994. "A Method for Modelling Varying Run-Off Evolutions in Claims Reserving," ASTIN Bulletin, Cambridge University Press, vol. 24(2), pages 325-332, November.
    3. England, P.D. & Verrall, R.J., 2002. "Stochastic Claims Reserving in General Insurance," British Actuarial Journal, Cambridge University Press, vol. 8(3), pages 443-518, August.
    4. Atherino, Rodrigo & Pizzinga, Adrian & Fernandes, Cristiano, 2010. "A Row-Wise Stacking of the Runoff Triangle: State Space Alternatives for IBNR Reserve Prediction," ASTIN Bulletin, Cambridge University Press, vol. 40(2), pages 917-946, November.
    5. Hendrych, Radek & Cipra, Tomas, 2021. "Applying State Space Models To Stochastic Claims Reserving," ASTIN Bulletin, Cambridge University Press, vol. 51(1), pages 267-301, January.
    6. Nataliya Chukhrova & Arne Johannssen, 2021. "Kalman Filter Learning Algorithms and State Space Representations for Stochastic Claims Reserving," Risks, MDPI, vol. 9(6), pages 1-5, June.
    7. Nataliya Chukhrova & Arne Johannssen, 2017. "State Space Models and the K alman -Filter in Stochastic Claims Reserving: Forecasting, Filtering and Smoothing," Risks, MDPI, vol. 5(2), pages 1-23, May.
    8. Taylor, G. C. & Ashe, F. R., 1983. "Second moments of estimates of outstanding claims," Journal of Econometrics, Elsevier, vol. 23(1), pages 37-61, September.
    9. Greg Taylor, 2019. "Loss Reserving Models: Granular and Machine Learning Forms," Risks, MDPI, vol. 7(3), pages 1-18, July.
    10. Ioannis Ntzoufras & Petros Dellaportas, 2002. "Bayesian Modelling of Outstanding Liabilities Incorporating Claim Count Uncertainty," North American Actuarial Journal, Taylor & Francis Journals, vol. 6(1), pages 113-125.
    11. Hertig, Joakim, 1985. "A Statistical Approach to IBNR-Reserves in Marine Reinsurance," ASTIN Bulletin, Cambridge University Press, vol. 15(2), pages 171-183, November.
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    Cited by:

    1. Gholamreza Hesamian & Arne Johannssen & Nataliya Chukhrova, 2023. "A Three-Stage Nonparametric Kernel-Based Time Series Model Based on Fuzzy Data," Mathematics, MDPI, vol. 11(13), pages 1-17, June.

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