In many insurance contexts, dependence between risks of a portfolio may arise from their frequencies. We investigate a dependent risk model in which we assume the vector of count variables to be a tree-structured Markov random field with Poisson marginals. The tree structure translates into a wide variety of dependence schemes. We study the global risk of the portfolio and the risk allocation to all its constituents. We provide asymptotic results for portfolios defined on infinitely growing trees. To illustrate its flexibility and computational scalability to higher dimensions, we calibrate the risk model on real-world extreme rainfall data and perform a risk analysis.

翻译：在许多保险情境下，投资组合中风险之间的依赖性可能源于其发生频率。我们研究了一个依赖风险模型，其中假设计数变量向量是一个具有泊松边际分布的树状结构马尔可夫随机场。这种树状结构衍生出多种多样的依赖模式。我们研究了投资组合的整体风险及其所有组成部分的风险分配。针对定义在无限增长树上的投资组合，我们提供了渐近结果。为了展示其在高维情形下的灵活性和计算可扩展性，我们将该风险模型应用于现实世界中的极端降雨数据，并进行了风险分析。