The problem of recovering the ruin probability in the classical risk model based on the scaled Laplace transform inversion is studied. It is shown how to overcome the problem of evaluating the ruin probability at large values of an initial surplus process. Comparisons of proposed approximations with the ones based on the Laplace transform inversions using a fixed Talbot algorithm as well as on the ones using the Trefethen-Weideman-Schmelzer and maximum entropy methods are presented via a simulation study.

中文翻译：

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使用缩放的拉普拉斯变换反演逼近破产概率

研究了基于尺度拉普拉斯变换反演的经典风险模型中破产概率的恢复问题。展示了如何克服在初始剩余过程的大值下评估破产概率的问题。通过模拟研究，将提议的近似值与基于使用固定 Talbot 算法的拉普拉斯变换反演的近似值以及使用 Trefethen-Weideman-Schmelzer 和最大熵方法的近似值进行比较。