带跳的Vasicek利率模型下的寿险净保费责任准备金  

Net premium reserve in life insurance under Vasicek model with jumps

作　　者：张彦国[1] 宋春燕 李世龙 ZHANG Yan-guo;SONG Chun-yan;LI Shi-long(School of Account,Shandong University of Finance and Economics,Jinan 250014,Shandong,China;School of Mathematic and Quantitative Economics,Shandong University of Finance and Economics,Jinan 250014,Shandong,China;School of Insurance,Shandong University of Finance and Economics,Jinan 250014,Shandong,China)

机构地区：[1]山东财经大学会计学院,山东济南250014 [2]山东财经大学数学与数量经济学院,山东济南250014 [3]山东财经大学保险学院,山东济南250014

出　　处：《山东大学学报（理学版）》2020年第9期81-88,共8页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(71671104);国家社会科学基金重点资助项目(16AZD019);山东省高校科技计划资助项目(J15LI01)。

摘　　要：基于市场利率的随机跳跃波动特征,利用复合Poisson过程和Ornstein-Uhlenbeck过程分别刻画利率的随机跳跃性和随机连续变化性,并将二者进行耦合构建具有随机跳跃性的利息力函数,得到一类带Poisson跳的Vasicek利率模型。研究在该利率模型下的累积利息力函数和货币期望折扣函数的数学表达形式,给出相应的数值分析,并基于此进一步研究了寿险产品净保费准备金的测算问题。Considering the characteristics of random volatility with jumps of market interest rates,both compound Poisson process and Ornstein-Uhlenbeck process are utilized to describe the stochastic jumps and random continuous changes of interest rates respectively.A Vasicek interest model with Poisson jumps is obtained by coupling the two kinds of stochastic processes.The mathematical expressions of the cumulative interest force function and the expected discount function of money under the model are studied.At the same time,the corresponding numerical analysis is given.Based on this interest model,the calculation of the net premium reserves of life insurance products is further studied.

关 键 词：随机利率模型 复合POISSON过程 ORNSTEIN-UHLENBECK过程 寿险 净保费责任准备金 

分 类 号：F224.7[经济管理—国民经济]