This paper investigates the optimal dividend problem in a jump-diffusion risk model with debit interest. In this model, the insurer could borrow money at a debit interest when the surplus turns negative. However, when the negative surplus attains a certain critical level, the business stops and absolute ruin happens at this moment. A sufficient condition under which the optimal dividend strategy is of barrier type is given in such a risk model. The main result relies on the smoothness of certain function arising from the dividend problem and we prove that it is twice continuously differentiable by the probability argument. Finally, numerical examples are given to illustrate the effects of the debit interest.

中文翻译：

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具有借方利息的跳跃-扩散风险模型中壁垒分红策略的最优性

本文研究了具有借方利息的跳跃扩散风险模型中的最优股息问题。在这个模型中，当盈余变为负值时，保险公司可以借入借方利息。但是，当负盈余达到一定临界水平时，业务停止，此时发生绝对破产。在这样的风险模型中，给出了最优分红策略为屏障类型的充分条件。主要结果依赖于由红利问题产生的某些函数的平滑性，我们证明它是由概率论证两次连续可微的。最后，通过数值例子说明借方利息的影响。