论文标题
使用Weibull分布的回火帕累托型建模
Tempered Pareto-type modelling using Weibull distributions
论文作者
论文摘要
在重尾建模的各种应用中，假定的帕累托行为最终在最大数据的范围内进行了纠正。在保险申请中，索赔付款受索赔管理的影响，例如，在最高损害水平的最高损害水平上，索赔可能会受到更高的检查水平，导致尾巴较弱，而不是模态索赔。概括Meerschaert等人的早期结果。 （2012）和Raschke（2019），在本文中，我们考虑在峰值阈值方法中以一般的韦布尔分布来调节帕累托型分布。这需要根据所选阈值调节回火参数。建模这种回火效果对于避免高估风险度量（例如高分位数的价值（VAR））很重要。我们使用伪最大似然方法来估计模型参数，并考虑对极端分位数的估计。我们为估计器得出了基本的渐近结果，通过模拟实验为插图提供了插图，并将开发的技术应用于启动和责任保险数据，从而深入了解了重型尾巴建模中回火组件的相关性。
In various applications of heavy-tail modelling, the assumed Pareto behavior is tempered ultimately in the range of the largest data. In insurance applications, claim payments are influenced by claim management and claims may for instance be subject to a higher level of inspection at highest damage levels leading to weaker tails than apparent from modal claims. Generalizing earlier results of Meerschaert et al. (2012) and Raschke (2019), in this paper we consider tempering of a Pareto-type distribution with a general Weibull distribution in a peaks-over-threshold approach. This requires to modulate the tempering parameters as a function of the chosen threshold. Modelling such a tempering effect is important in order to avoid overestimation of risk measures such as the Value-at-Risk (VaR) at high quantiles. We use a pseudo maximum likelihood approach to estimate the model parameters, and consider the estimation of extreme quantiles. We derive basic asymptotic results for the estimators, give illustrations with simulation experiments and apply the developed techniques to fire and liability insurance data, providing insight into the relevance of the tempering component in heavy-tail modelling.
