中文摘要：

该文主要讨论带扰动的经典风险模型中当索赔服从次指数分布时贴现罚函数的渐近表达式.得到两种情形下由索赔引起的贴现罚函数的精确表达式.此外,证明当初始盈余趋近无穷时由扰动引起的贴现罚函数可以忽略.

英文摘要：

In this paper,the authors focus on asymptotic behavior of the discounted penalty function in the classical risk model perturbed by diffusion when the claim size is sub-exponentially distributed.They obtain the exact asymptotic expressions for the discounted penalty function caused by a claim,in two cases：δ〉0 andδ=0,whereδdenotes the interest force.Moreover, it is showed that the discounted penalty function caused by oscillation vanishes when the initial reserve goes to infinity.