In the random environment with diffusion,we consider the Cox risk model with a premium rate which varies according to the intensity of claims. By using the renewal argument and stochastic analysis method,we obtain the defective renewal equation,the series expression,the asymptotic property of the penalty function.%在带有扰动的随机环境中,考虑保费率随索赔强度而变化的Cox风险模型,利用更新论证及随机分析的方法,得到了罚金函数的瑕疵更新方程、级数表达式和渐近性质,推广了文献[3]中关于破产概率的相应结果,于是可以根据罚金函数的不同形式,给出保险公司所关心的更多精算变量的级数表达式与渐近性质。最后也给出了罚金函数的几个特例及其相应结果。
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