带两类离散时间风险过程的期望折现罚金函数

The Expected Discounted Penalty Function for the Two Classes of Discrete Time Risk Processes

对带两种独立类型的保险风险的离散时间风险模型,我们假设第一类的索赔间隔时间是服从几何分布的随机变量,第二类索赔间隔时间是两个相互独立的各自服从几何分布的随机变量的总和,当两类的赔款服从几何分布时可以得到Gerber-Shiu期望折现罚金函数的表达式.由定义的Dickson-Hipp算子,得到罚金函数的简化表达式.

To the discrete risk model of the two independent classes of insurance risks,in the author’s opinion,it is assumed that the claiming spacing interval of the first class is the random variable submitting to the geometric distribution,and the claiming spacing interval of the second class is the sum of the two mutually independent random variables submitting to geometric distribution.The Gerber-Shiu expected stochastic premium expression can be obtained when the indemnity of the two classes obey the geometric distributions.Defined by the Dickson-Hipp operator,the simplified expression of the penalty function is obtained.