具有随机保费的风险模型下的平均折现罚金函数On the expected discounted penalty function associated with the time of ruin for a risk model with random

 具有随机保费的风险模型下的平均折现罚金函数 [EB/OL]

北京：中国科技论文在线

） 摘要： 本文考虑随机保费的风险模型下平均折现罚金函数

关键词： 随机保费, 复合泊松分布, 罚金函数, 破产时刻, 破产前瞬时盈余,破产时赤字

Cram$\\\\\\\\acute{\\\\\\\\mbox{e}}$r-Lundberg model

The aggregate premiums constitute a compound Poisson process which is also independent of the claim process

Integral equation for the penalty function is derived, which provides a unified treatment to the ruin quantities

Applications of the integral equation are given to the Laplace transform of the time of ruin, the deficit at ruin,the surplus immediately before ruin occurs

In some special cases with exponential distributions, closed form expressions for these quantities are obtained, which generalize some known results about the problems of ruin in Boikov(2003)

Keywords： stochastic premium,integral equation,penalty function,the time of ruin, the deficit at ruin, the surplus immediately before ruin occurs

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本文得到了罚金函数所满足的积分方程, 在指数分布的条件下

与经典的风险模型相比较保费过程不再是线性过程

利用该积分方程分别得到了破产时刻、破产前瞬时盈余和破产时赤字的折现期望的显著表达式

） Abstract： This paper studies the expected discounted penalty function associated with the time of ruin for a risk model with stochastic premium

The premium process is no longer a linear function of time in contrast with the classical