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A Markov Model for Loss Reserving

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  • Hesselager, Ole

Abstract

The claims generating process for a non-life insurance portfolio is modelled as a marked Poisson process, where the mark associated with an incurred claim describes the development of that claim until final settlement. An unsettled claim is at any point in time assigned to a state in some state-space, and the transitions between different states are assumed to be governed by a Markovian law. All claims payments are assumed to occur at the time of transition between states. We develop separate expressions for the IBNR and RBNS reserves, and the corresponding prediction errors.

Suggested Citation

  • Hesselager, Ole, 1994. "A Markov Model for Loss Reserving," ASTIN Bulletin, Cambridge University Press, vol. 24(2), pages 183-193, November.
    • Handle: RePEc:cup:astinb:v:24:y:1994:i:02:p:183-193_00
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    Cited by:

    1. Maciak, Matúš & Okhrin, Ostap & Pešta, Michal, 2021. "Infinitely stochastic micro reserving," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 30-58.
    2. Benjamin Avanzi & Gregory Clive Taylor & Melantha Wang & Bernard Wong, 2020. "SynthETIC: an individual insurance claim simulator with feature control," Papers 2008.05693, arXiv.org, revised Aug 2021.
    3. Francis Duval & Mathieu Pigeon, 2019. "Individual Loss Reserving Using a Gradient Boosting-Based Approach," Risks, MDPI, vol. 7(3), pages 1-18, July.
    4. Arthur Charpentier & Mathieu Pigeon, 2016. "Macro vs. Micro Methods in Non-Life Claims Reserving (an Econometric Perspective)," Risks, MDPI, vol. 4(2), pages 1-18, May.
    5. Avanzi, Benjamin & Taylor, Greg & Wang, Melantha & Wong, Bernard, 2021. "SynthETIC: An individual insurance claim simulator with feature control," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 296-308.
    6. Emmanuel Jordy Menvouta & Jolien Ponnet & Robin Van Oirbeek & Tim Verdonck, 2022. "mCube: Multinomial Micro-level reserving Model," Papers 2212.00101, arXiv.org.
    7. Greg Taylor, 2019. "Loss Reserving Models: Granular and Machine Learning Forms," Risks, MDPI, vol. 7(3), pages 1-18, July.
    8. Jiandong Ren, 2016. "Analysis of Insurance Claim Settlement Process with Markovian Arrival Processes," Risks, MDPI, vol. 4(1), pages 1-10, March.
    9. Yining Feng & Shuanming Li, 2023. "Advancing the Use of Deep Learning in Loss Reserving: A Generalized DeepTriangle Approach," Risks, MDPI, vol. 12(1), pages 1-14, December.
    10. Mat'uv{s} Maciak & Ostap Okhrin & Michal Pev{s}ta, 2019. "Infinitely Stochastic Micro Forecasting," Papers 1908.10636, arXiv.org, revised Sep 2019.

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