This paper develops asymptotics and approximations for ruin probabilities in a multivariate risk setting. We consider a model in which the individual reserve processes are driven by a common Markovian environmental process. We subsequently consider a regime in which the claim arrival intensity and transition rates of the environmental process are jointly sped up, and one in which there is (with overwhelming probability) maximally one transition of the environmental process in the time interval considered. The approximations are extensively tested in a series of numerical experiments.

中文翻译：

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马氏环境中多元风险过程的破产概率的渐近性和逼近性

本文研究了多元风险情况下破产概率的渐近和近似。我们考虑一个模型，其中单个储备过程受共同的马尔可夫环境过程驱动。随后，我们考虑一种机制，在这种机制中，环境过程的索赔到达强度和过渡速度共同加快，在考虑的时间间隔内，（以压倒性的可能性）最大程度地发生环境过程的一种过渡。在一系列数值实验中，对近似值进行了广泛的测试。