In this paper, we revisit the finite-time ruin probability in the classical compound Poisson risk model. Traditional general solutions to finite-time ruin problems are usually expressed in terms of infinite sums involving the convolutions related to the claim size distribution and their integrals, which can typically be evaluated only in special cases where the claims follow exponential or (more generally) mixed Erlang distribution. We propose to tackle the partial integro-differential equation satisfied by the finite-time ruin probability and develop a new approach to obtain a solution in terms of bivariate Laguerre series as a function of the initial surplus level and the time horizon for a large class of light-tailed claim distributions. To illustrate the versatility and accuracy of our proposed method which is easy to implement, numerical examples are provided for claim amount distributions such as generalized inverse Gaussian, Weibull and truncated normal where closed-form convolutions are not available in the literature.

在本文中，我们重新审视了经典复合泊松风险模型中的有限时间破产概率。有限时间破产问题的传统一般解决方案通常用涉及与索赔规模分布及其积分相关的卷积的无限和表示，通常只能在索赔遵循指数或（更一般地）混合的特殊情况下进行评估二郎分布。我们建议解决由有限时间破产概率满足的偏积分微分方程，并开发一种新方法来根据作为初始盈余水平和时间范围的函数的二元拉盖尔级数获得解决方案大类轻尾索赔分布。为了说明我们提出的易于实施的方法的通用性和准确性，