通胀风险下基于HARA效用的DC型养老金计划
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摘要
通货膨胀是养老基金管理过程中最直接最重要的影响因素之一.假设通胀风险由服从几何布朗运动的物价指数来度量,且瞬时期望通货膨胀率由Ornstein-Uhlenbeck过程来驱动.金融市场由n+1种可连续交易的风险资产所构成,养老基金管理者期望研究和解决通胀风险环境下DC型养老基金在累积阶段的最优投资策略问题,以最大化终端真实财富过程的期望效用.双曲绝对风险厌恶(HARA)效用函数具有一般的效用框架,包含幂效用、指数效用和对数效用作为特例.假设投资者对风险的偏好程度满足HARA效用,运用随机最优控制理论和Legendre变换方法得到了最优投资策略的显式表达式.
Inflation risk is one of the most direct and important influential factors in the process of pension fund scheme management.In this paper,inflation risk is supposed to be measured by price index satisfying geometric Brownian motion.And instantaneous expected inflation rate is assumed to be driven by Ornstein-Uhlenbeck process.The fund manager plans to invest his real wealth in the financial market composed of multiple risky assets and expect to maximize expected utility of terminal real wealth.His goal is to obtain the optimal investment strategy for defined contribution pension fund scheme in the accumulation phase.Hyperbolic absolute risk aversion(HARA) utility function is of general utility framework and consists of power utility,exponential utility and logarithmic utility as specific cases.This paper supposes the risky aversion degree of fund manager to satisfy HARA utility and uses stochastic dynamic programming principle along with Legendre transform-dual theory to successfully obtain the closed-form expression of the optimal investment strategy.In addition,some special cases are derived in detail.
Inflation risk is one of the most direct and important influential factors in the process of pension fund scheme management.In this paper,inflation risk is supposed to be measured by price index satisfying geometric Brownian motion.And instantaneous expected inflation rate is assumed to be driven by Ornstein-Uhlenbeck process.The fund manager plans to invest his real wealth in the financial market composed of multiple risky assets and expect to maximize expected utility of terminal real wealth.His goal is to obtain the optimal investment strategy for defined contribution pension fund scheme in the accumulation phase.Hyperbolic absolute risk aversion(HARA) utility function is of general utility framework and consists of power utility,exponential utility and logarithmic utility as specific cases.This paper supposes the risky aversion degree of fund manager to satisfy HARA utility and uses stochastic dynamic programming principle along with Legendre transform-dual theory to successfully obtain the closed-form expression of the optimal investment strategy.In addition,some special cases are derived in detail.
引文
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[12]谷爱玲,李仲飞,曾燕.Ornstein-Uhlenbeck模型下DC养老金计划的最优投资策略[J].应用数学学报,2013,36:715-726.
[13]伍慧玲,董洪斌.带有通胀风险和随机收入的确定缴费养老计划[J].系统工程理论与实践,2016,36:545-558.
[14]Jung E J,Kim J H.Optimal investment strategies for the HARA utility under the constant elasticity of variance model[J].Insurance:Mathematics and Economics,2012,51:667-673
[15]Chang H,Rong X M.Legendre transform-dual solution for a class of investment and consumption problems with HARA utility[J].Mathematical Problems in Engineering,2014,2014(4):1-7.
[16]Chang H,Chang K,Lu J M.Portfolio selection with liability and affine interest rate in the HARA utility framework[J].Abstract and Applied Analysis,2014,2014:1-12.
[17]Jonsson M,Sircar R.Optimal investment problems and volatility homogenization approximations[M]//Modern Methods in Scientific Computing and Applications,Berlin:Springer,2002,255-281.
[18]Gao J W.An extended CEV model and the Legendre transform dual asymptotic solutions for annuity contracts[J].Insurance:Mathematics and Economics,2010,46:511-530.
[2]Deelstra G,Grasselli M,Koehl P F.Optimal investment strategies in the presence of a minimum guarantee[J].Insurance:Mathematics and Economics,2003,33:189-207.
[3]Xiao J W,Zhai H,Qin C L.The constant elasticity of variance(CEV)model and the Legendre transform-dual solution for annuity contracts[J].Insurance:Mathematics and Economics,2007,40:302-310.
[4]Gao J W.Optimal portfolios for DC pension plans under a CEV model[J].Insurance:Mathematics and Economics,2009,44:479-490.
[5]Zhang A H,Ewald C O.Optimal investment for a pension fund under inflation risk[J].Mathematical Methods of Operations Research,2010,71:353-369.
[6]Han N W,Hung M W.Optimal asset allocation for DC pension plans under inflation[J].Insurance:Mathematics and Economics,2012,51:172-181.
[7]Yao H X,Yang Z,Chen P.Markowitz's mean-variance defined contribution pension fund management under inflation:a continuous-time model[J].Insurance:Mathematics and Economics,2013,53:851-863.
[8]Guan G H,Liang Z X.Optimal management of DC pension plan in a stochastic interest rates and stochastic volatility framework[J].Insurance:Mathematics and Economics,2014,57:58-66.
[9]Guan G H,Liang Z X.Mean-variance efficiency of DC pension plan under stochastic interest rate and mean-reverting returns[J].Insurance:Mathematics and Economics,2015,61:99-109.
[10]Li D P,Rong X M,Zhao H.Time-consistent investment strategy for DC pension plan with stochastic salary under CEV model[J].Journal of Systems Science and Complexity,2016,29:428-454.
[11]殷俊,李嫒嫒.基于随机利率和通货膨胀的缴费确定型养老金计划最优资产配置策略[J].当代经济科学,2013,35:11-20.
[12]谷爱玲,李仲飞,曾燕.Ornstein-Uhlenbeck模型下DC养老金计划的最优投资策略[J].应用数学学报,2013,36:715-726.
[13]伍慧玲,董洪斌.带有通胀风险和随机收入的确定缴费养老计划[J].系统工程理论与实践,2016,36:545-558.
[14]Jung E J,Kim J H.Optimal investment strategies for the HARA utility under the constant elasticity of variance model[J].Insurance:Mathematics and Economics,2012,51:667-673
[15]Chang H,Rong X M.Legendre transform-dual solution for a class of investment and consumption problems with HARA utility[J].Mathematical Problems in Engineering,2014,2014(4):1-7.
[16]Chang H,Chang K,Lu J M.Portfolio selection with liability and affine interest rate in the HARA utility framework[J].Abstract and Applied Analysis,2014,2014:1-12.
[17]Jonsson M,Sircar R.Optimal investment problems and volatility homogenization approximations[M]//Modern Methods in Scientific Computing and Applications,Berlin:Springer,2002,255-281.
[18]Gao J W.An extended CEV model and the Legendre transform dual asymptotic solutions for annuity contracts[J].Insurance:Mathematics and Economics,2010,46:511-530.