两因子随机死亡率状态空间模型及长寿风险测度  

A Two Factor State-space Model for Stochastic Mortality and Longevity Risk Measurement

作　　者：何颖媛[1,2] 刘贯春[1] 

机构地区：[1]中南大学商学院,湖南长沙410083 [2]长沙学院工商管理系,湖南长沙410085

出　　处：《财经理论与实践》2014年第5期24-28,共5页The Theory and Practice of Finance and Economics

基　　金：湖南省社科基金项目(13YBA030);湖南省社科基金项目(11YBB039);国家自然科学基金项目(71203241)

摘　　要：引入状态空间模型对传统两因子CBD模型拟合阶段和预测阶段进行联合建模,并基于卡尔曼滤波方法对模型参数进行估计。进一步考虑到死亡率数据的小样本特征,结合Bootstrap仿真技术和生存年金组合折现模型对长寿风险进行测度。利用1996~2011年数据展开实证研究,结果表明：结合模型解释能力、参数估计结果和误差项正态分布检验结果,两因子状态空间模型要优于传统CBD模型;年金组合规模的扩大可以消除微观长寿风险,但不能消除宏观长寿风险和参数风险;宏观长寿风险占据着不可分散风险的主导地位。To model the fitting and forecasting stages of traditional CBD method jointly, we formulate a state-space framework, and use the Kalman filtering technique to estimate it. Further, considering the small sample characteristics of mortality data, we propose an approach to measuring longevity risk by combining Bootstrap simulation and portfolios of life annuities. Specifically, longevity risk includes mi- cro-/macro-longevity risk, and parameter risk. Empirical results of Chinese mortality show that the new model is superior to the traditional CBD model in terms of model explanation power, estimation accuracy and normal distribution tests for errors. The expansion of annuity portfolio can eliminate the micro-long evity risk, but it cannot eliminate the macro-longevity risk and the parameter risk. Meanwhile, the mac- ro-longevity risk dominates the non-removable risk.

关 键 词：状态空间模型 卡尔曼滤波估计 Bootstrap仿真 长寿风险 

分 类 号：F840.32[经济管理—保险]