Estimating Quantile Families of Loss Distributions for Non-Life Insurance Modelling via L-Moments
Estimating Quantile Families of Loss Distributions for Non-Life Insurance Modelling via L-Moments
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通过 L 矩估计非寿险建模损失分布的分位数族
DOI：
10.2139/ssrn.2739417
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
R. Gerlach
中科院分区：
文献类型：
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作者：
G. Peters;W. Chen;R. Gerlach
本文讨论了非寿险环境下不同类别的损失模型。然后概述了一类在非寿险建模中尚未被广泛考虑的Tukey变换损失模型，但提供了产生损失建模中经常需要的灵活偏度和峰度特征的机会。此外，这些损失模型承认明确的分位数规范，这使得它们与基于分位数的风险度量计算直接相关。我们详细介绍了基于Tukey变换的模型的各种参数化和子族，例如g和h， g和k以及g和j模型，包括它们与损失建模相关的属性。当拟合这样的模型时，从业者面临的挑战之一是对模型参数进行稳健估计。在本文中，我们开发了一种新颖，高效，鲁棒的方法来估计这类Tukey变换模型的参数，基于l -矩。结果表明，对于此类损失模型族，该方法比目前最先进的估计方法更有效，同时在实际应用中易于实现。
This paper discusses different classes of loss models in non-life insurance settings. It then overviews the class of Tukey transform loss models that have not yet been widely considered in non-life insurance modelling, but offer opportunities to produce flexible skewness and kurtosis features often required in loss modelling. In addition, these loss models admit explicit quantile specifications which make them directly relevant for quantile based risk measure calculations. We detail various parameterisations and sub-families of the Tukey transform based models, such as the g-and-h, g-and-k and g-and-j models, including their properties of relevance to loss modelling. One of the challenges that are amenable to practitioners when fitting such models is to perform robust estimation of the model parameters. In this paper we develop a novel, efficient, and robust procedure for estimating the parameters of this family of Tukey transform models, based on L-moments. It is shown to be more efficient than the current state of the art estimation methods for such families of loss models while being simple to implement for practical purposes.