We analyze the classical Brownian risk models discussing the approximation of ruin probabilities (classical, γ-reflected, Parisian and cumulative Parisian) for the case that ruin can occur only on specific discrete grids. A practical and natural grid of points is for instance , which allows us to study the probability of the ruin on the first day, second day, and so one. For such a discrete setting, there are no explicit formulas for the ruin probabilities mentioned above. In this contribution we derive accurate approximations of ruin probabilities for uniform grids by letting the initial capital to grow to infinity.

中文翻译：

---

离散布朗风险模型中破产概率和破产时间的近似

我们分析了经典布朗风险模型，讨论了破产概率的近似值（经典的、γ 反射的、巴黎的和累积的巴黎），因为破产只能发生在特定的离散网格上。例如，一个实用且自然的点网格是 ，它允许我们研究第一天、第二天等等的废墟的概率。对于这样一个离散的设置，上面提到的破产概率没有明确的公式。在这个贡献中，我们通过让初始资本增长到无穷大来推导出均匀网格的破产概率的准确近似值。