The aim of this paper is to construct the confidence interval of the ultimate ruin probability under the insurance surplus driven by a L\'evy process. Assuming a parametric family for the L\'evy measures, we estimate the parameter from the surplus data and estimate the ruin probability via the delta method. However the asymptotic variance includes the derivative of the ruin probability with respect to the parameter, which is not generally given explicitly, and the confidence interval is not straightforward even if the ruin probability is well estimated. This paper gives the Cram\'er-type approximation for the derivative and gives an asymptotic confidence interval of ruin probability.

翻译：本文的目的是构建由 L\'evy 过程驱动的保险顺差下最终残废概率的置信度间隔。 假设L\' evy 测量值的参数组, 我们根据剩余数据估算参数, 并通过三角洲方法估算残废概率。 但是, 无保护差异包括该参数的废损概率的衍生物, 而该参数一般没有明确给出, 而置信度间隔并不直截了当, 即使对废机概率做了很好的估计 。 本文给出了衍生物的Cram\'er类型近似值, 并给出了无保障的断存概率间隔 。