Especially , we investigate a local asymptotic behavior of the probability of ruin which individual claims size have a distribution that belongs to s ( v ) with v > 0 . the main results : theorem 2 . 3 . 2 let satisfies the defective renewal equation , where theorem 2 . 3 . 2 the ruin probability ( u ) has the following expression ( 2 . 3 . 3 ) where 7 ( 11 ) is defined in theorem 2 . 2 . 2 and dx 1时，罚金折现期望厂’ … ）便为最终破产概率（山（叫） ，所以破产概率也满足一高阶积分一微分方程；由此得到了破产概率的拉普拉斯变换，从而得到了破产概率所满足的一股疵的更新方程
Then we get ruin probability , actuarial diagnostics and lundberg inequality in the new model . as to the risk model with random premium rate , we concerned with discrete random variable , continuous random variable and general random variable . we derive the formula of ruin probability , the extreme during the total duration of negative surplus and the joint distribution of the surplus immediately before ruin and the deficit at ruin 对于保费率为随机变量的一类风险模型，本文就离散的随机变量、连续的随机变量、一般的随机变量三个方面进行讨论，运用概率方法和风险理论的方法推导出破产概率、末离前最大盈余分布、破产前瞬时盈余与破产赤字的联合分布等精算量分布的一般公式。
