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arXiv · 1806.05939

Generalized Log-Normal Chain-Ladder

D. Kuang·B. Nielsen
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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.

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D. Kuang, B. Nielsen. 2018-06-15. Generalized Log-Normal Chain-Ladder. https://arxiv.org/abs/1806.05939

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