随机时间变换下的寿险精算模型  

Life actuary models under time deformation

作　　者：于栋华[1] 吴冲锋[1] 陈湘鹏[1] 

机构地区：[1]上海交通大学安泰经济与管理学院,上海200030

出　　处：《管理科学学报》2010年第6期64-72,共9页Journal of Management Sciences in China

摘　　要：时间变换方法广泛应用于经济学和金融学领域中,但在保险方面几乎没有涉及.而某些保险问题往往在等间隔的日历时间下的统计性质非常复杂,但是却可以找到某个适度的经济时间,使得在该经济时间标度下,保险问题具有简单清晰的统计结构.因此,引入时间变换方法,就可以简化保险问题.首次将时间变换引入寿险问题中,提出了一种新型的保险产品设计思路,即按照经济时间设计保险产品.给出了经济时间标度下的相应寿险模型的定义、计算,并通过对等价利息力的定义,讨论了不同时间标度下寿险模型的转换关系.最后,进一步给出了时间变换下破产概率问题的结果.本模型可以应用于很多实践问题.Although time deformation methods are widely used in the fields of Economics and Finance, it rarely appears in the fields of insurance. It is noticed that under the calendar time some problems in insurance have very complicated statistical properties in equal intervals. But we can find a proper time scale named economical time and under this new time scale, these problems will now have simple and explicit statistical structures. So, by the introduction of time deformation, we can simplify the structures of insurance problems. In this paper, we apply time deformation methods into the fields of life insurance for the first time and propose a new idea for designing insurance products. That is： to design insurance products under the economical time scale. First we give the definition and calculation methods under the scale of economical time for actuary models including whole life insurances, whole life annuities and the according premiums and reserves, etc. , and then we concentrate on the relationships between different scales and give the definition of equivalent interest force. We find that the equivalent interest force is an important instrument for time deformation. Finally, we give the result of the ruin probability under time deformation. Our models can be applied in many practical situations.

关 键 词：时间变换 生命保险 生存年金 破产概率 

分 类 号：F840.62[经济管理—保险]