In this paper, we model the insurance company's surplus flow by a perturbed compound Poisson model. Suppose that at a sequence of random time points, the insurance company observes the surplus to decide dividend payments. If the observed surplus level is larger than the maximum of a threshold $ b>0 $ and the last observed level (after dividends payment if possible), then a fraction $ 0<\theta<1 $ of the excess amount is paid out as a lump sum dividend. We assume that the solvency is also discretely monitored at these observation times, so that the surplus process stops when the observed value becomes negative. Integro-differential equations for the expected discounted dividend payments before ruin and the Gerber-Shiu expected discounted penalty function are derived, and solutions are also analyzed by Laplace transform method. Numerical examples are given to illustrate the applicability of our results.

中文翻译：

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周期阈值型股利策略下的复合泊松风险模型

在本文中，我们通过扰动复合泊松模型对保险公司的盈余流进行建模。假设保险公司在一系列随机时间点观察盈余来决定股息支付。如果观察到的剩余水平大于阈值$ b> 0 $和最后一个观察到的水平（如果可能的话，在派发股息之后）的最大值，则支付剩余金额的一部分$ 0 <\ theta <1 $作为一次性分红。我们假设在这些观察时间还对偿付能力进行了离散监控，因此当观察值变为负值时，剩余过程将停止。推导了破产前预期折现股利支付的积分微分方程和Gerber-Shiu预期折现罚金函数，并使用拉普拉斯变换法分析了解。