摘要翻译：
本文从对数正态链梯模型出发，提出了一个分布预测的渐近理论。该理论克服了对数正态变量卷积的困难，并考虑了估计误差。结果不同于过分散泊松模型和基于链梯的Bootstrap模型。将对数正规链梯模型嵌入到一类无限可分分布中，称为广义对数正规链梯模型。渐近理论采用小σ-渐近理论，其中保留三角形的维数保持不变，同时假定标准差减小。所得的渐近预报分布服从t分布。该理论得到了仿真和实证应用的支持。
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英文标题：
《Generalized Log-Normal Chain-Ladder》
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作者：
D. Kuang and B. Nielsen
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最新提交年份：
2018
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分类信息：

一级分类：Statistics        统计学
二级分类：Methodology        方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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一级分类：Economics        经济学
二级分类：Econometrics        计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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英文摘要：
  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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PDF链接：
https://arxiv.org/pdf/1806.05939