关键词: 索赔额, 正态分布, 破产概率, 渐近估计, 显式解

Abstract: In the case of individual sum of claim obey a normal distribution，we use mathematical risk theory and classical probability theory corresponding theories and methods to construct a mathematical model. Finally，the insurance company's ultimate ruin probability explicit expression is derived out，and its asymptotic estimate is obtained based on the explicit solutions.

Key words: amount of the claim, normal distribution, ruin probability, asymptotic estimation, explicit expression