论文标题
模型错误及其估计，特别适用于保留损失
Model error and its estimation, with particular application to loss reserving
论文作者
论文摘要
本文涉及预测错误，尤其是与保留损失有关的错误。这通常被认为是由三个组件组成的，即参数，过程和模型错误。这些组件中的前两个及其估计值众所周知，但模型误差较少。模型错误本身在两个部分中考虑：一个部分能够从过去的数据（内部模型错误）中估算的一部分，而不是另一部分（外部模型错误）。注意力集中在内部模型错误上。使用贝叶斯对套索的解释，通过贝叶斯模型平均来了解此误差分量的估计。这用于生成一组可允许的模型，每个模型的先前概率和观察到的数据的可能性。模型集的后验，根据数据误差的数据，结果和模型误差的估计（包含在损失储备中）的估计值作为损失储备的差异，该方差根据此后验。实质性地进入后部支持的模型可能比所需的稀薄，而套索的自举来获得批量。这也提供了参数误差估计值的奖励。事实证明，参数错误和模型错误的估计是纠缠的，它们的解离至少很困难，甚至可能没有意义。讨论了这些问题。大多数讨论通常适用于预测，但是有关保险数据和保险保留问题的数字说明是给出概念的。
This paper is concerned with forecast error, particularly in relation to loss reserving. This is generally regarded as consisting of three components, namely parameter, process and model errors. The first two of these components, and their estimation, are well understood, but less so model error. Model error itself is considered in two parts: one part that is capable of estimation from past data (internal model error), and another part that is not (external model error). Attention is focused here on internal model error. Estimation of this error component is approached by means of Bayesian model averaging, using the Bayesian interpretation of the LASSO. This is used to generate a set of admissible models, each with its prior probability and the likelihood of observed data. A posterior on the model set, conditional on the data, results, and an estimate of model error (contained in a loss reserve) is obtained as the variance of the loss reserve according to this posterior. The population of models entering materially into the support of the posterior may turn out to be thinner than desired, and bootstrapping of the LASSO is used to gain bulk. This provides the bonus of an estimate of parameter error also. It turns out that the estimates of parameter and model errors are entangled, and dissociation of them is at least difficult, and possibly not even meaningful. These matters are discussed. The majority of the discussion applies to forecasting generally, but numerical illustration of the concepts is given in relation to insurance data and the problem of insurance loss reserving.
