免赔额影响下的风险过程

Risk process under deductible

在古典风险过程中引入免赔额,认为保费的收取与免赔额有关且是免赔额的减函数,并考虑相应风险过程的破产概率。当损失分布服从指数分布时,可以得到破产概率的一个简洁表达式,从表达式可以看出,免赔额的增加可以有效降低破产概率;从数值角度比较不同免赔额下的破产概率也可以发现,引入免赔额可降低破产概率和保费,有利于扩大参保人数。

Deductible is introduced into the classical risk process, and it is thought that premium cohection not only relates to deductible but also is a decreasing function of deductible. In the mean time, the ruin probability of the risk process is also taken into consideration. When the loss is exponential distribution, a concise expression of ruin probability can be got, and the expression shows that the ruin probability is obviously decreasing with the increase of deductible ; when the ruin probabilities with different deductibles are compared from a numerical angle, it is found that introducing deductible not only decreases the ruin probability and premium but also increases the number of insured person.