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Generalized Log-Normal Chain-Ladder

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  • D. Kuang
  • B. Nielsen

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 $\sigma$ 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," Papers 1806.05939, arXiv.org.
    • Handle: RePEc:arx:papers:1806.05939
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    File URL: http://arxiv.org/pdf/1806.05939
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    References listed on IDEAS

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    1. Verrall, R. J., 1991. "On the estimation of reserves from loglinear models," Insurance: Mathematics and Economics, Elsevier, vol. 10(1), pages 75-80, March.
    2. 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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    1. D. Kuang & B. Nielsen, 2018. "Generalized Log-Normal Chain-Ladder," Economics Papers 2018-W02, Economics Group, Nuffield College, University of Oxford.
    2. D Kuang & Bent Nielsen & J P Nielsen, 2013. "The Geometric Chain-Ladder," Economics Papers 2013-W11, Economics Group, Nuffield College, University of Oxford.
    3. Jonas Harnau, 2018. "Log-Normal or Over-Dispersed Poisson?," Risks, MDPI, vol. 6(3), pages 1-37, July.
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