中文摘要：

该文讨论了带常利率复合Poisson风险模型中的预警区问题．在此，作者提出了一种新的方法，其有别于Gerber于1990年提出的鞅方法，通过这种新方法，最终得到了负盈余持续时间的矩母函数及各阶矩，进而在索赔指数情形给出了精确解析式，并利用计算得到的数值结果讨论了利率变化对预警区的影响．

英文摘要：

In this paper, the authors discuss the duration of negative surplus of the classical compound Poisson risk model with constant interest force. By presenting a new approach different from the martingale method proposed by Gerber （1990）, the moment generating functions and the moments of both the single and total duration of negative surplus are formulated. Explicit expressions are given when the claim is exponentially distributed. Finally, the influence of interest force on the duration of negative surplus is illustrated by numerical results.