基于混合密度神经网络的随机损失准备金
Stochastic loss reserving with mixture density neural networks
摘要：
神经网络为损失准备金提供了一种通用、灵活和准确的方法。然而，这类申请主要侧重于对未决索赔作出准确的中心估计这一（重要）问题。在实践中，关于未决索赔的可变性的性质同样重要（例如，用于监管目的的分位数）。在本文中，我们填补了这一空白，应用混合密度网络（“MDN”）的损失准备金。该方法结合了神经网络结构与混合高斯分布，同时实现了准确的中心估计以及灵活的分布选择。模型拟合使用滚动原点方法完成。我们的方法始终优于经典的过度分散模型的中心估计和分位数的利益，当应用到各种复杂性和规格的模拟环境。我们进一步扩展MDN的方法，提出了两个扩展。首先，我们提出了一种混合GLM-MDN方法称为“ResMDN”。这种混合方法一方面平衡了传统GLM模型的易处理性和易于理解性，另一方面又平衡了MDN提供的额外准确性和分布灵活性。我们表明，它可以成功地改善基线ccODP的错误，虽然在我们考虑的示例中，与MDN相比，通常会有性能损失。其次，我们允许明确的预测约束，使精算判断可以直接纳入建模过程。在整个过程中，我们专注于总损失三角形，并表明我们的方法是易于处理的，即使在数据量相对有限的情况下，它们也优于传统方法。我们使用模拟数据-验证属性，和真实的数据-来说明和确定的方法的实用性。
英文摘要：
Neural networks offer a versatile, flexible and accurate approach to loss reserving. However, such applications have focused primarily on the (important) problem of fitting accurate central estimates of the outstanding claims. In practice, properties regarding the variability of outstanding claims are equally important (e.g., quantiles for regulatory purposes). In this paper we fill this gap by applying a Mixture Density Network ("MDN") to loss reserving. The approach combines a neural network architecture with a mixture Gaussian distribution to achieve simultaneously an accurate central estimate along with flexible distributional choice. Model fitting is done using a rolling-origin approach. Our approach consistently outperforms the classical over-dispersed model both for central estimates and quantiles of interest, when applied to a wide range of simulated environments of various complexity and specifications. We further extend the MDN approach by proposing two extensions. Firstly, we present a hybrid GLM-MDN approach called "ResMDN". This hybrid approach balances the tractability and ease of understanding of a traditional GLM model on one hand, with the additional accuracy and distributional flexibility provided by the MDN on the other. We show that it can successfully improve the errors of the baseline ccODP, although there is generally a loss of performance when compared to the MDN in the examples we considered. Secondly, we allow for explicit projection constraints, so that actuarial judgement can be directly incorporated in the modelling process. Throughout, we focus on aggregate loss triangles, and show that our methodologies are tractable, and that they out-perform traditional approaches even with relatively limited amounts of data. We use both simulated data -- to validate properties, and real data -- to illustrate and ascertain practicality of the approaches.
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