“中人”历史债务的双随机模型

Dual Random Model of the History Debt of Category Ⅱ

在人寿保险和年金保险中,死亡率和利息率是两个极为重要的随机因素。传统的精算理论假定利率为确定而仅讨论死亡率为随机的情形。然而事实上,利息率具有随机性。本文为社会养老保险制度转轨过程中的"中人"历史债务建立双随机模型(死亡率和利息率均为随机),得到了"中人"历史债务现值的期望值,并对息力累积函数以Wiener过程和O U过程建模得到了期望值的具体表达式。最后做了一个实例,以浙江省某市的实际数据,估算了该市的"中人"历史债务额。

This paper discusses the history debt during the transformation of social pension insurance in China.The dual random model of the present value of the history debt of Category Ⅱ who took part in work before the new social insurance system and will retire after that has been set.The first moment of the present value of the history debt has been calculated,and the concrete expressions of the moments have been calculated when the force of interest accumulation function is Wiener process and Ornstein-Uhlenbeck process respectively.Finally,we calculate the history debt of a city in Zhejiang with the actual data.