Parisian ruin probability in the classical Brownian risk model, unlike the standard ruin probability can not be explicitly calculated even in one-dimensional setup. Resorting on asymptotic theory, we derive in this contribution the asymptotic approximations of both Parisian and cumulative Parisian ruin probabilities and simultaneous ruin time for the two-dimensional Brownian risk model when the initial capital increases to infinity.

中文翻译：

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二维布朗风险模型的巴黎和累积巴黎破产概率

经典布朗风险模型中的巴黎破产概率，与标准破产概率不同，即使在一维设置中也无法明确计算。借助渐近理论，我们在此贡献中推导出当初始资本增加到无穷大时二维布朗风险模型的巴黎和累积巴黎破产概率以及同时破产时间的渐近近似。