A discrete-time risk model with a mathematically tractable dependence structure between interclaim times and claim sizes is considered in the presence of an impulsive dividend strategy. Under such a strategy, once the insurer's reserve upcrosses the level b, the excess of the reserve over is paid off as dividends. We derive difference equations for both the expected discounted penalty function and the expected present value of dividend payments. Solution procedures for these difference equations are provided. When the joint distribution of the interclaim time and claim size is a finite mixture of bivariate geometric distributions, closed-form expressions are given. Numerical results for several sets of parameters are also provided to illustrate the applicability of the results obtained.

中文翻译：

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具有时间相关索赔和冲动股息支付的离散时间风险模型

在存在冲动分红策略的情况下，考虑了一个离散时间风险模型，该模型在索赔时间和索赔规模之间具有数学上易于处理的依赖结构。在这种策略下，一旦保险公司的准备金超过 b 级，多余的准备金将作为红利支付。我们推导出预期贴现惩罚函数和预期股息支付现值的差分方程。提供了这些差分方程的求解过程。当索赔间期和索赔额的联合分布是二元几何分布的有限混合时，给出闭式表达式。还提供了几组参数的数值结果，以说明所得结果的适用性。