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Generalized Log-Normal Chain-Ladder

Author

Listed:
  • D. Kuang

    (Lloyd's of London)

  • B. Nielsen

    (Nuffield College, University of Oxford)

Abstract

We propose an asymptotic theory for distribution forecasting from the log normal chain-ladder model. The theory overcomes the difficulty of convoluting log normal variables and takes estimation error into account. The results differ from that of the over-dispersed Poisson model and from the chain-ladder based bootstrap. We embed the log normal chain-ladder model in a class of infinitely divisible distributions called the generalized log normal chain-ladder model. The asymptotic theory uses small σ asymptotics where the dimension of the reserving triangle is kept fixed while the standard deviation is assumed to decrease. The resulting asymptotic forecast distributions follow t distributions. The theory is supported by simulations and an empirical application.

Suggested Citation

  • D. Kuang & B. Nielsen, 2018. "Generalized Log-Normal Chain-Ladder," Economics Papers 2018-W02, Economics Group, Nuffield College, University of Oxford.
    • Handle: RePEc:nuf:econwp:1802
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    File URL: https://www.nuffield.ox.ac.uk/economics/Papers/2018/2018W02_KuangNielsen2018GLNCL.pdf
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    References listed on IDEAS

    as
    1. D. Kuang & B. Nielsen & J. P. Nielsen, 2008. "Forecasting with the age-period-cohort model and the extended chain-ladder model," Biometrika, Biometrika Trust, vol. 95(4), pages 987-991.
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    Cited by:

    1. Jonas Harnau, 2018. "Misspecification Tests for Log-Normal and Over-Dispersed Poisson Chain-Ladder Models," Risks, MDPI, vol. 6(2), pages 1-25, March.
    2. Jonas Harnau, 2018. "Log-Normal or Over-Dispersed Poisson?," Risks, MDPI, vol. 6(3), pages 1-37, July.

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