We present a universal methodology for bounding multidimensional ultimate ruin probabilities $\mathbf{\Psi }$ in regime-switching models. Some new lower and upper bounds on $\mathbf{\Psi }$ are given. The considered methods are applicable to several discrete- and continuous time risk models. As an example, we construct a variety of new two-sided operator bounds which converge to $\mathbf{\Psi }$ with an exponential rate. Several numerical examples are also provided.

中文翻译：

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在政权转换模型中界定多维破产概率的一般方法

我们提出了一种通用的方法来界定多维最终破产概率 $\mathbf{\Psi }$在政权转换模型中。一些新的下限和上限$\mathbf{\Psi }$给出。所考虑的方法适用于多个离散和连续时间风险模型。例如，我们构造了各种新的两侧算子边界，它们收敛到$\mathbf{\Psi }$以指数速率。还提供了几个数值示例。