基于Lee-Carter模型的互助养老年金研究
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摘要
基于经典的双线性随机Lee-Carter模型,采用经济学的协整理论,对中国大陆男性人口死亡率进行预测,克服了ARIMA模型预测的局限性.在随机利率和Lee-Carter模型的基础上度量退休年金和生命年金的长寿风险,并为此提出应对策略,引入由消费者承担系统长寿风险、年金池承担个体长寿风险的群体自助养老年金(GSA),然后对其进行实证分析发现,与普通年金相比,GSA模型分担模式拥有较高的给付额.
The co-integration theory of economics combined with the classical bilinear random Lee-Carter model was used to fit and forecast the male population mortality in Mainland China,and solved the limitations of the ARIMA model.Meanwhile,the two kinds of longevity risk about retirement pension and life annuity were measured,which based on the stochastic interest rate and Lee-Carter model.Then the model of the Group Self-pooling Annuitization(GSA)in which the system longevity risk was borne by consumers,and the individual longevity risk was borne by the annuity pool.The result showed that the model of GSA had a higher payment compare with the ordinary pension.
The co-integration theory of economics combined with the classical bilinear random Lee-Carter model was used to fit and forecast the male population mortality in Mainland China,and solved the limitations of the ARIMA model.Meanwhile,the two kinds of longevity risk about retirement pension and life annuity were measured,which based on the stochastic interest rate and Lee-Carter model.Then the model of the Group Self-pooling Annuitization(GSA)in which the system longevity risk was borne by consumers,and the individual longevity risk was borne by the annuity pool.The result showed that the model of GSA had a higher payment compare with the ordinary pension.
引文
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[2]JONG P D,TICKLE L,XU J H.Coherent modeling of male and female mortality using Lee-Carter in a complex number framework[J].Insurance:Mathematics and Economics,2016(71):130-137.
[3]CALLOT L,HALDRUP N,LAMB M K.Deterministic and stochastic trends in the Lee-Carter mortalitymodel[J].Applied Economics Letters,2016,23(7):486-493.
[4]YANG S S,WANG C W.Pricing and securitization of multicountry longevity risk with mortality dependence[J].Insurance:Mathematics and Economics,2013,52(2):157-169.
[5]张奕,王婷婷.基于协整理论的中国人口死亡率预测[J].高校应用数学学报(A辑),2015(1):1-9.
[6]吴晓坤,李姚洁.Lee-Carter模型外推预测死亡率及偏差纠正[J].统计与决策,2016(20):19-21.
[7]曾燕,陈曦,邓颖璐.创新的动态人口死亡率预测及其应用[J].系统工程理论与实践,2016,36(7):1710-1718.
[8]PIGGOTT J,VALDEZ E A,DEZEL B.The simple analytics of a pooled annuity fund[J].Journal of Risk and Insurance,2005,72(3):497-520.
[9]FORMAN J B,SABIN M J.Using tontines to solve public pension underfunding[J].Pensions and Investments,2014,42(12):11-18.
[10]ENGLE R F,GRANGER C W.Co-integration and error correction:representation,estimation,and testing[J].Econometric:Journal of the Econometric Society,1987,55(2):251-276.
[11]QIAO C,SHERRIS M.Managing systematic mortality risk with group self-pooling and annuitization schemes[J].The Journal of Risk and Insurance,2013,80(4):949-974.
[2]JONG P D,TICKLE L,XU J H.Coherent modeling of male and female mortality using Lee-Carter in a complex number framework[J].Insurance:Mathematics and Economics,2016(71):130-137.
[3]CALLOT L,HALDRUP N,LAMB M K.Deterministic and stochastic trends in the Lee-Carter mortalitymodel[J].Applied Economics Letters,2016,23(7):486-493.
[4]YANG S S,WANG C W.Pricing and securitization of multicountry longevity risk with mortality dependence[J].Insurance:Mathematics and Economics,2013,52(2):157-169.
[5]张奕,王婷婷.基于协整理论的中国人口死亡率预测[J].高校应用数学学报(A辑),2015(1):1-9.
[6]吴晓坤,李姚洁.Lee-Carter模型外推预测死亡率及偏差纠正[J].统计与决策,2016(20):19-21.
[7]曾燕,陈曦,邓颖璐.创新的动态人口死亡率预测及其应用[J].系统工程理论与实践,2016,36(7):1710-1718.
[8]PIGGOTT J,VALDEZ E A,DEZEL B.The simple analytics of a pooled annuity fund[J].Journal of Risk and Insurance,2005,72(3):497-520.
[9]FORMAN J B,SABIN M J.Using tontines to solve public pension underfunding[J].Pensions and Investments,2014,42(12):11-18.
[10]ENGLE R F,GRANGER C W.Co-integration and error correction:representation,estimation,and testing[J].Econometric:Journal of the Econometric Society,1987,55(2):251-276.
[11]QIAO C,SHERRIS M.Managing systematic mortality risk with group self-pooling and annuitization schemes[J].The Journal of Risk and Insurance,2013,80(4):949-974.