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Kalman Filter Learning Algorithms and State Space Representations for Stochastic Claims Reserving

Author

Listed:
  • Nataliya Chukhrova

    (Faculty of Business Administration, University of Hamburg, 20146 Hamburg, Germany
    The authors contributed equally to this work.)

  • Arne Johannssen

    (Faculty of Business Administration, University of Hamburg, 20146 Hamburg, Germany
    The authors contributed equally to this work.)

Abstract

In stochastic claims reserving, state space models have been used for almost 40 years to forecast loss reserves and to compute their mean squared error of prediction. Although state space models and the associated Kalman filter learning algorithms are very powerful and flexible tools, comparatively few articles on this topic were published during this period. Most recently, several articles have been published which highlight the benefits of state space models in stochastic claims reserving and may lead to a significant increase in its popularity for applications in actuarial practice. To further emphasize the merits of these papers, this commentary highlights various additional aspects that are useful for practical applications and offer some fruitful directions for future research.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jrisks:v:9:y:2021:i:6:p:112-:d:569870
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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. Avanzi, Benjamin & Taylor, Greg & Vu, Phuong Anh & Wong, Bernard, 2020. "A multivariate evolutionary generalised linear model framework with adaptive estimation for claims reserving," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 50-71.
    3. Benjamin Avanzi & Gregory Clive Taylor & Phuong Anh Vu & Bernard Wong, 2020. "A multivariate evolutionary generalised linear model framework with adaptive estimation for claims reserving," Papers 2004.06880, arXiv.org.
    4. Francis Duval & Mathieu Pigeon, 2019. "Individual Loss Reserving Using a Gradient Boosting-Based Approach," Risks, MDPI, vol. 7(3), pages 1-18, July.
    5. Massimo De Felice & Franco Moriconi, 2019. "Claim Watching and Individual Claims Reserving Using Classification and Regression Trees," Risks, MDPI, vol. 7(4), pages 1-36, October.
    6. 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.
    7. Avanzi, Benjamin & Taylor, Greg & Wong, Bernard, 2018. "Common Shock Models For Claim Arrays," ASTIN Bulletin, Cambridge University Press, vol. 48(3), pages 1109-1136, September.
    8. 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.
    9. 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.
    10. 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.
    11. Leonardo Costa & Adrian Pizzinga, 2020. "State‐space models for predicting IBNR reserve in row‐wise ordered runoff triangles: Calendar year IBNR reserves & tail effects," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(3), pages 438-448, April.
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    Cited by:

    1. Nataliya Chukhrova & Arne Johannssen, 2021. "Stochastic Claims Reserving Methods with State Space Representations: A Review," Risks, MDPI, vol. 9(11), pages 1-55, November.

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