论文标题
关于具有COX过程和依赖射击噪声强度的多元计数的建模
On the modelling of multivariate counts with Cox processes and dependent shot noise intensities
论文作者
论文摘要
在本文中，我们开发了一种使用粒状数据建模和估算几个_依赖性计数过程的方法。具体而言，我们开发了一个具有射击噪声强度的多元COX流程，以共同对计数的到达过程进行建模（例如，保险索赔）。依赖性结构是通过借助莱维·库拉斯（LévyCopulas）连接的多变量射击噪声_intsente _intsenty _ intions_ Intios _intentys_引入的。总体而言，我们的方法允许（i）在每种业务行中进行过度分散和自动相关； （ii）涉及随时间变化的已知协变量的现实特征； （iii）过程之间的偏见依赖性，而无需同时发生事件（例如事故）事件。 随时间变化的已知协变量的明确合并可以适应真实数据的特征，从而促进实践实施。在保险环境中，这些可能是随着时间的流逝的保单量的变化以及季节性的模式和趋势，这可能解释了多个索赔过程之间的某些关系（依赖性），或者至少有助于取消这些关系。 最后，我们基于可逆的跳跃马尔可夫链蒙特卡洛（RJMCMC）方法开发了一种过滤算法，以估计潜在的随机强度，并使用来自AUSI数据集的实际数据来说明模型校准。
In this paper, we develop a method to model and estimate several, _dependent_ count processes, using granular data. Specifically, we develop a multivariate Cox process with shot noise intensities to jointly model the arrival process of counts (e.g. insurance claims). The dependency structure is introduced via multivariate shot noise _intensity_ processes which are connected with the help of Lévy copulas. In aggregate, our approach allows for (i) over-dispersion and auto-correlation within each line of business; (ii) realistic features involving time-varying, known covariates; and (iii) parsimonious dependence between processes without requiring simultaneous primary (e.g. accidents) events. The explicit incorporation of time-varying, known covariates can accommodate characteristics of real data and hence facilitate implementation in practice. In an insurance context, these could be changes in policy volumes over time, as well as seasonality patterns and trends, which may explain some of the relationship (dependence) between multiple claims processes, or at least help tease out those relationships. Finally, we develop a filtering algorithm based on the reversible-jump Markov Chain Monte Carlo (RJMCMC) method to estimate the latent stochastic intensities and illustrate model calibration using real data from the AUSI data set.
