In this paper, the classical compound Poisson model under periodic observation is studied. Different from the random observation assumption widely used in the literature, we suppose that the inter-observation time is a constant. In this model, both the finite-time and infinite-time Gerber-Shiu functions are studied via the Laguerre series expansion method. We show that the expansion coefficients can be recursively determined and also analyze the approximation errors in detail. Numerical results for several claim size density functions are given to demonstrate effectiveness of our method, and the effect of some parameters is also studied.

中文翻译：

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具有恒定观测间时间的复合泊松模型中的 Gerber-Shiu 分析

本文研究了周期观测下的经典复合泊松模型。与文献中广泛使用的随机观察假设不同，我们假设观察间隔时间是一个常数。在此模型中，有限时间和无限时间 Gerber-Shiu 函数均通过拉盖尔级数展开法进行了研究。我们表明可以递归确定扩展系数，并详细分析了近似误差。给出了几个索赔规模密度函数的数值结果来证明我们的方法的有效性，并且还研究了一些参数的影响。