到达时间条件分布在风险理论中的一个应用

The conditional distribution of the arrival time in application of risk theroy

考虑保险公司经营的两类险种的保险业务:Ⅰ型和Ⅱ型.这两类险种的理赔次数过程N1(t)和N2(t)是相互独立的计数过程,且其理赔额序列Xi和Yi均服从截尾指数分布,则利用到达时间分布可得到该保险公司随时间变化两类险种的平均理赔额。

We consider two types of insurance business in insurance company： type and type . The two claim number processes and are independent counting processes, and the two claims and are subject to the truncated exponential distribution. Eventually we obtain the average amount of claims of the two types of insurance over time.