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On the classical risk model with credit and debit interests under absolute ruin

机译：绝对破产情况下含借方和贷方利息的经典风险模型

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摘要

In this paper, we consider the dividend payments in a compound Poisson risk model with credit and debit interests under absolute ruin. We first obtain the integro-differential equations satisfied by the moment generating function and moments of the discounted aggregate dividend payments. Secondly, applying these results, we get the explicit expressions of them for exponential claims. Then, we give the numerical analysis of the optimal dividend barrier and the expected discounted aggregate dividend payments which are influenced by the debit and credit interests. Finally, we find the integro-differential equations satisfied by the Laplace transform of absolute ruin time and give its explicit expressions when the claim sizes are exponentially distributed.
机译：在本文中，我们考虑在绝对破产的情况下，具有贷方和借方利息的复合Poisson风险模型中的股利支付。我们首先获得由矩生成函数和折现总股利支付的矩所满足的积分微分方程。其次，应用这些结果，我们得到了指数要求的显式表达式。然后，我们对受借方和贷方利息影响的最佳股息壁垒和预期折现总股息支付进行了数值分析。最后，我们找到了绝对毁灭时间的拉普拉斯变换所满足的积分-微分方程，并在索赔额呈指数分布时给出了其明确的表达式。

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