arXiv 15 Jun 2018 · Statistics — Methodology · publishedScandinavian Actuarial Journal (2019) · 8 citations (OpenAlex)
arXiv:1806.05939 · PDF · DOI · OpenAlex · Extracted main text
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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