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State Space Models and the K alman -Filter in Stochastic Claims Reserving: Forecasting, Filtering and Smoothing

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  • 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

This paper gives a detailed overview of the current state of research in relation to the use of state space models and the K alman -filter in the field of stochastic claims reserving. Most of these state space representations are matrix-based, which complicates their applications. Therefore, to facilitate the implementation of state space models in practice, we present a scalar state space model for cumulative payments, which is an extension of the well-known chain ladder (CL) method. The presented model is distribution-free, forms a basis for determining the entire unobservable lower and upper run-off triangles and can easily be applied in practice using the K alman -filter for prediction, filtering and smoothing of cumulative payments. In addition, the model provides an easy way to find outliers in the data and to determine outlier effects. Finally, an empirical comparison of the scalar state space model, promising prior state space models and some popular stochastic claims reserving methods is performed.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jrisks:v:5:y:2017:i:2:p:30-:d:99880
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. Kevin Kuo, 2019. "DeepTriangle: A Deep Learning Approach to Loss Reserving," Risks, MDPI, vol. 7(3), pages 1-12, September.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Nguyen, Trang & Chaiechi, Taha & Eagle, Lynne & Low, David, 2020. "Dynamic transmissions between main stock markets and SME stock markets: Evidence from tropical economies," The Quarterly Review of Economics and Finance, Elsevier, vol. 75(C), pages 308-324.
    8. Nataliya Chukhrova & Arne Johannssen, 2021. "Stochastic Claims Reserving Methods with State Space Representations: A Review," Risks, MDPI, vol. 9(11), pages 1-55, November.
    9. Valandis Elpidorou & Carolin Margraf & María Dolores Martínez-Miranda & Bent Nielsen, 2019. "A Likelihood Approach to Bornhuetter–Ferguson Analysis," Risks, MDPI, vol. 7(4), pages 1-20, December.

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