DC型养老金积累期最优资产配置问题研究
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摘要
DC型养老金积累期长达数十年,如何通过合理的资产配置,实现资金的有效增值是重要的问题。本文建立了DC型养老金个人账户积累额变动的连续时间随机模型,该模型综合考虑了投资收益、缴费效应和生存者利益对积累额的影响。同时,积累期结束时积累额能够满足养老金给付接近目标替代率被选取为优化目标。利用HJB变分方法等随机控制的方法与理论,得到了积累期最优资产配置策略的解析解。利用Monte Carlo模拟方法证明,积累期缴费率对在风险资产的配置比例有负向影响;目标替代率、人口老龄化程度以及对正向偏差的偏好程度对风险资产的配置比例有正向影响。
The accumulation phase of the Defined Contribution pension plan lasts for decades. How to choose appropriate asset allocation strategies to increase the accumulation effectively is an important issue. In this paper,we established the continuous time stochastic model of the dynamics of the accumulation of individual account. The investment return,contribution effect and the mortality credit were all considered in the model. Minimization of the actual and expected accumulation with target wage substitution rate was considered the optimal objective. Using HJB variational methods,the closed forms of the optimal allocation policies were established. Furthermore,we used Monte Carlo methods to prove that the contribution rate and the proportion allocated to the risk assets had negative correlations,while the target substitutionrate,the severity of the aging problem and the preference of positive deviation were positively correlated with the proportion allocated to the risk assets.
The accumulation phase of the Defined Contribution pension plan lasts for decades. How to choose appropriate asset allocation strategies to increase the accumulation effectively is an important issue. In this paper,we established the continuous time stochastic model of the dynamics of the accumulation of individual account. The investment return,contribution effect and the mortality credit were all considered in the model. Minimization of the actual and expected accumulation with target wage substitution rate was considered the optimal objective. Using HJB variational methods,the closed forms of the optimal allocation policies were established. Furthermore,we used Monte Carlo methods to prove that the contribution rate and the proportion allocated to the risk assets had negative correlations,while the target substitutionrate,the severity of the aging problem and the preference of positive deviation were positively correlated with the proportion allocated to the risk assets.
引文
[1]Shapiro,A.F.:Contribution to the Evolution of Pension Cost Analysis.[J]Journal of Risk and Insurance,Vol.52,p81-99,1985.
[2]Brinson,G.P.,Singer,B.D.,Gilbert,L.and Beebower,G.L.:Determinants of Portfolio Performance II:An Update.[J]Financial Analysis Journal,Vol.47,p40-48,1991.
[3]Merton,R.C.:Optimum Consumption and Portfolio Rules in a Continuous-time Model.[J]Journal of Economic Theory,Vol.3,p373-413,1971.
[4]Battocchio,P.and Menoncin,F.:Optimal Pension Management in a Stochastic Framework.[J]Insurance:Mathematics and Economics,Vol.34,p79-95,2004.
[5]翟永会,王晓芳,闫海峰.企业年金积累期的最优动态资产配置策略[J].中国管理科学,2010,(10)。
[6]Ngwira,B.and Gerrard,R.:Stochastic Pension Fund Control in the Presence of Poisson Jumps.[J]Insurance:Mathematics and Economics,Vol.40,p238-292,2007.
[7]Gao,J.:Stochastic Optimal Control of DC Pension Funds.[J]Insurance:Mathematics and Economics,Vol.42,p1159-1164,2008.
[8]郭磊,陈方正.退休后企业年金基金最优投资决策[J].系统科学,Vol.24,78-82,2006。
[9]Devolder,P.,Borch Princep,M.and Dominguez Fabian,I:Stochastic Optimal Control of Annuity Contracts.[J]Insurance:Mathematics and Economics,Vol.33,p227-238,2003.
[10]张初兵,荣喜民.均值-方差模型下DC型养老金的随机最优控制[J].系统工程理论与实践,Vol.32,1314-1323,2012。
[11]Bordley,R.and Li Calzi,M.:Decision Analysis Using Targets Instead of Utility Functions.[J]Decision in E-conomics and Finance,Vol.23,p53-74,2000.
[12]Vigna,E.and Haberman,S.:Optimal Investment Strategy for Defined Contribution Pension Scheme.[J]Insurance:Mathematics and Economics,Vol.28,p233-262,2001.
[13]Chang,S.C.,Tzeng,L.Y.and Miao,J.C.Y.:Pension Funding Incorporating Downside Risks.[J]Insurance:Mathematics and Economics,Vol.32,217-228,2003.
[14]Cairns,A.J.G.,Blake,D.and Dowd,K.:Stochastic Lifestyling:Optimal Dynamic Asset Allocation for Defined Contribution Pension Plans.[J]Journal of Economic Dynamics and Control,Vol.30,p843-877,2006.
[15]Lions,P.L.and Sznitman,A.S.:Stochastic Differential Equations with Reflecting Boundary Conditions,[J]Comm.Pure Appl.Math.,Vol.37,511-537,1984.
[16]Φksendal,B.and Sulem,A.:Applied Stochastic Control of Jump Diffusions,2ndEdition,Springer,ISBN:3540698256.
[17]He,L.and Liang,Z.X.:Optimal Asset Allocation and Benefit Outgo Policies of DC Pension Plan with Compulsory Conversion Claims.[J]Insurance:Mathematics and Economics,Vol.61,p227-234,2015.
[2]Brinson,G.P.,Singer,B.D.,Gilbert,L.and Beebower,G.L.:Determinants of Portfolio Performance II:An Update.[J]Financial Analysis Journal,Vol.47,p40-48,1991.
[3]Merton,R.C.:Optimum Consumption and Portfolio Rules in a Continuous-time Model.[J]Journal of Economic Theory,Vol.3,p373-413,1971.
[4]Battocchio,P.and Menoncin,F.:Optimal Pension Management in a Stochastic Framework.[J]Insurance:Mathematics and Economics,Vol.34,p79-95,2004.
[5]翟永会,王晓芳,闫海峰.企业年金积累期的最优动态资产配置策略[J].中国管理科学,2010,(10)。
[6]Ngwira,B.and Gerrard,R.:Stochastic Pension Fund Control in the Presence of Poisson Jumps.[J]Insurance:Mathematics and Economics,Vol.40,p238-292,2007.
[7]Gao,J.:Stochastic Optimal Control of DC Pension Funds.[J]Insurance:Mathematics and Economics,Vol.42,p1159-1164,2008.
[8]郭磊,陈方正.退休后企业年金基金最优投资决策[J].系统科学,Vol.24,78-82,2006。
[9]Devolder,P.,Borch Princep,M.and Dominguez Fabian,I:Stochastic Optimal Control of Annuity Contracts.[J]Insurance:Mathematics and Economics,Vol.33,p227-238,2003.
[10]张初兵,荣喜民.均值-方差模型下DC型养老金的随机最优控制[J].系统工程理论与实践,Vol.32,1314-1323,2012。
[11]Bordley,R.and Li Calzi,M.:Decision Analysis Using Targets Instead of Utility Functions.[J]Decision in E-conomics and Finance,Vol.23,p53-74,2000.
[12]Vigna,E.and Haberman,S.:Optimal Investment Strategy for Defined Contribution Pension Scheme.[J]Insurance:Mathematics and Economics,Vol.28,p233-262,2001.
[13]Chang,S.C.,Tzeng,L.Y.and Miao,J.C.Y.:Pension Funding Incorporating Downside Risks.[J]Insurance:Mathematics and Economics,Vol.32,217-228,2003.
[14]Cairns,A.J.G.,Blake,D.and Dowd,K.:Stochastic Lifestyling:Optimal Dynamic Asset Allocation for Defined Contribution Pension Plans.[J]Journal of Economic Dynamics and Control,Vol.30,p843-877,2006.
[15]Lions,P.L.and Sznitman,A.S.:Stochastic Differential Equations with Reflecting Boundary Conditions,[J]Comm.Pure Appl.Math.,Vol.37,511-537,1984.
[16]Φksendal,B.and Sulem,A.:Applied Stochastic Control of Jump Diffusions,2ndEdition,Springer,ISBN:3540698256.
[17]He,L.and Liang,Z.X.:Optimal Asset Allocation and Benefit Outgo Policies of DC Pension Plan with Compulsory Conversion Claims.[J]Insurance:Mathematics and Economics,Vol.61,p227-234,2015.