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.

在本文中，我们开发了一种使用粒度数据来建模和估计多个相关计数过程的方法。具体来说，我们开发了一种具有散粒噪声强度的多元Cox过程，以共同对计数的到达过程（例如，保险索赔）进行建模。通过多变量散粒噪声强度过程引入依赖结构，该过程在Lévycopulas的帮助下进行连接。总体而言，我们的方法允许（i）每个业务领域内的过度分散和自相关；（ii）涉及时变，已知协变量的现实特征；（iii）过程之间的简约依赖，而无需同时发生主要（例如事故）事件。

时变的已知协变量的显式合并可以适应实际数据的特征，因此便于在实践中实施。在保险的情况下，这些可能是保单量随时间的变化以及季节性模式和趋势，这可能解释了多个索赔流程之间的某些关系（依存关系），或者至少有助于弄清这些关系。

最后，我们开发了一种基于可逆跳跃马尔可夫链蒙特卡罗（RJMCMC）方法的滤波算法，以估计潜在随机强度并说明使用来自AUSI数据集的真实数据进行模型校准。