论文标题
多元布朗风险模型中的大流行型失败
Pandemic-type Failures in Multivariate Brownian Risk Models
论文作者
论文摘要
从大流行型事件的角度来看，对保险，金融和应用概率的其他领域的多个同时失败建模很重要。用于分析多个故障的基准限制模型是经典的$ d $ d $二维风险模型（BRM），请参见[1]。从理论和实际的角度来看，感兴趣的是计算给定时间范围内多个同时失败的概率。这项贡献的主要发现涉及近似BRM的$ d $组件中至少$ k $同时失败的概率。我们得出了有限时间和无限时间范围感兴趣的概率的尖锐边界和渐近近似。我们的结果扩展了[2,3]的先前发现。
Modelling of multiple simultaneous failures in insurance, finance and other areas of applied probability is important especially from the point of view of pandemic-type events. A benchmark limiting model for the analysis of multiple failures is the classical $d$-dimensional Brownian risk model (Brm), see [1]. From both theoretical and practical point of view, of interest is the calculation of the probability of multiple simultaneous failures in a given time horizon. The main findings of this contribution concern the approximation of the probability that at least $k$ out of $d$ components of Brm fail simultaneously. We derive both sharp bounds and asymptotic approximations of the probability of interest for the finite and the infinite time horizon. Our results extend previous findings of [2,3].
