用Cox过程和相关散粒噪声强度模拟多元计数
On the modelling of multivariate counts with Cox processes and dependent shot noise intensities
摘要：
在本文中，我们开发了一种方法来建模和估计几个，依赖计数过程，使用粒度数据。具体来说，我们开发了一个多变量Cox过程与散粒噪声强度共同建模计数（如保险索赔）的到达过程。利用Lévy Copula函数将多变量散粒噪声强度过程连接起来，引入了相关结构.总的来说，我们的方法允许（i）每个业务线内的过度分散和自相关性;（ii）涉及时变、已知协变量的现实特征;以及（iii）过程之间的简约依赖性，而不需要同时的主要（例如事故）事件。明确纳入随时间变化的，已知的协变量可以适应真实数据的特性，从而促进在实践中的实施。在保险方面，这些可能是保单数量随时间的变化，以及季节性模式和趋势，这可以解释多个索赔流程之间的一些关系（依赖性），或者至少有助于梳理这些关系。最后，我们开发了一个过滤算法的基础上的可逆跳马尔可夫链蒙特卡罗（RJMCMC）方法来估计潜在的随机强度和说明模型校准使用真实数据从AUSI数据集。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
