死亡率和通胀风险下的DC型养老金最优投资
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摘要
针对非系统性风险(死亡率风险)和系统性风险(通货膨胀风险)在DC型养老金最优投资策略中产生的影响,提出了基于死亡率风险和通货膨胀下对冲负债的DC型养老金最优投资策略问题,其中死亡率危险和通货膨胀风险是相互独立的因素;假设养老金缴费成员退休前将养老金投资于股票市场和银行,通货膨胀、投资股票和银行的收益、成员工资以及养老金负债均为随机过程,死亡率预测采用Lee-Carter模型;建立连续时间下的对冲负债的DC型养老金动态价值模型,结合随机控制理论推出对应的HJB方程,利用Legendre转化法得到基于死亡率和通货膨胀风险下对冲负债的DC型养老金最优投资比例,最后通过数值模拟分析得到最优投资策略随着投资期限的增加受到通货膨胀风险的影响大于死亡率风险所产生的影响。
According to the influence of non-systemic risk( mortality risk) and systemic risk( inflation risk)on the optimal investment of DC pension,among which mortality and inflation risk are independent of each other,the optimal investment strategy issue of DC pension hedging liability based on mortality risk and inflation is proposed. This paper assumes that the pension players invest their pension in stock market and banks before retirement,that inflation,returns from the investment in stock and banks,members' salaries and pension liabilities are all stochastic process and that Lee-Carter Model is used to predict mortality,therefore,a DC pension dynamic value model for hedging liabilities under continuous time is established,the corresponding HJB equation is derived in the combination with stochastic control theory,and the optimal investment proportion of DC pension hedging liabilities based on mortality and inflation risk is obtained by using Legendre transform method. Finally,through numerical simulation,the paper analyzes the influence of the optimal investment strategy on the inflation risk more than on mortality risk with the increasing of investment period.
According to the influence of non-systemic risk( mortality risk) and systemic risk( inflation risk)on the optimal investment of DC pension,among which mortality and inflation risk are independent of each other,the optimal investment strategy issue of DC pension hedging liability based on mortality risk and inflation is proposed. This paper assumes that the pension players invest their pension in stock market and banks before retirement,that inflation,returns from the investment in stock and banks,members' salaries and pension liabilities are all stochastic process and that Lee-Carter Model is used to predict mortality,therefore,a DC pension dynamic value model for hedging liabilities under continuous time is established,the corresponding HJB equation is derived in the combination with stochastic control theory,and the optimal investment proportion of DC pension hedging liabilities based on mortality and inflation risk is obtained by using Legendre transform method. Finally,through numerical simulation,the paper analyzes the influence of the optimal investment strategy on the inflation risk more than on mortality risk with the increasing of investment period.
引文
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[14]张静.确定给付型养老金计划的资产配置动态优化模型[D].北京:北京大学,2006ZHANG J. Dynamic Optimization Model of the Asset Allocation of the Contributory Pension[D]. Beijing:Peking University,2006
[15]吴涛,马田.中国债券市场的风险控制困境与化解[J].重庆工商大学学报(自然科学版),2017,34(5):9—17WU T,MA T. Resolution for the Dilemma of Risk Control in Chinese Bond Market[J]. Journal of Chongqing Technology and Business University(Natural Science Edition),2017,34(5):9—17
[2] DERBALI A. Systemic Risk in the Chinese Financial System:Measuring and Ranking[J]. The Chinese Economy,2017,50(1):34—58
[3] ZHANG A,EWALD C O. Optimal Investment for a Pension Fund under Inflation Risk[J]. Mathematical Methods of Operations Research, 2010, 71(2):353—369
[4] HAN N W,HUNG M W. Optimal Asset Allocation for DC Pension Plans under Inflation[J]. Insurance:Mathematics and Economics,2012,51(1):172—181
[5]安鹏.基于随机利率和通货膨胀的养老金资产配置[D].上海:上海交通大学,2009AN P. Optimal Asset Alloction for Pension Funds with Stochastic Interest Rate and Inflation[D]. Shanghai:Shanghai Jiaotong University,2009
[6]卞世博,刘海龙.背景风险下DC型养老基金的最优投资策略—基于Legendre转换对偶解法[J].管理工程学报,2013,27(3):145—149BIAN S B, LIU H L. An Application of Legendre Transform-dual Solutions for DC Pension Funds Optimal Investment Strategy under Background Risk[J]. Journal of Industrial Engineering,2013,27(3):145—149
[7] YAO H X,LAI Y Z,MA Q H,et al. Asset Allocation for a DC Pension Fund with Stochastic Income and Mortality Risk:A Multi-period Mean-variance Framework[J].Insurance:Mathematics and Economics, 2014, 54:84—92
[8] LIANG Z X,MA M. Optimal Dynamic Asset Allocation of Pension Fund in Mortality and Salary Risks Framework[J]. Insurance:Mathematics and Economics, 2015(64):151—161
[9] ARO H. Systematic and Nonsystematic Mortality Risk in Pension Portfolios[J].North American Actuarial Journal,2014,18(1):59—67
[10]霍忻,刘黎明.基于ARIMA模型的中国“十三五”时期通货膨胀率波动趋势研究[J].新疆社会科学,2017(5):33—40HUO X,LIU L M. A Study on the Fluctuation Trend of Inflation Rate in the 13th Five-year Plan Period in China Based on the ARIMA Model[J]. Social Sciences in Xinjiang,2017(5):33—40
[11]谷雨婷.中国人口死亡率预测方法研究[D].大连:东北财经大学,2011GU Y T. Prediction Methods of Chinesse Population Mortality[D]. Dalian:Dongbei University of Finance and Economics,2011
[12]李仲飞,陈峥.带有随机收入与时变风险厌恶系数的最优投资—消费问题[J].系统工程理论与实践,2017,37(7):1166—1178LI Z F,CHEN Z. Optimal Investment and Consumption Choice with Stochastic Income and Time-varying Risk Aversion[J]. Systems Engineering Theory&Practice,2017,37(7):1166—1178
[13]蒲兴成,张毅.随机微分方程及其在数理金融中的应用[M].北京:科学出版社,2010PU X C, ZHANG Y. Stochastic Equation and Its application in Mathematical Finance[M]. Beijing:Science Press,2010
[14]张静.确定给付型养老金计划的资产配置动态优化模型[D].北京:北京大学,2006ZHANG J. Dynamic Optimization Model of the Asset Allocation of the Contributory Pension[D]. Beijing:Peking University,2006
[15]吴涛,马田.中国债券市场的风险控制困境与化解[J].重庆工商大学学报(自然科学版),2017,34(5):9—17WU T,MA T. Resolution for the Dilemma of Risk Control in Chinese Bond Market[J]. Journal of Chongqing Technology and Business University(Natural Science Edition),2017,34(5):9—17