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：在许多保险情境中，投资组合中各风险间的相关性可能源于其发生频率。本文研究一种相依风险模型，其中假设计数变量向量为具有泊松边缘分布的树结构马尔可夫随机场。树结构可转化为多种相依模式。我们考察投资组合的整体风险及其对所有构成部分的风险配置。针对定义在无限增长树上的投资组合，我们给出了渐近结果。为说明该模型在高维情形下的灵活性与计算可扩展性，我们基于真实极端降雨数据对风险模型进行校准并执行风险分析。