考虑通胀指数债券的最优投资-闲暇与自愿退休选择
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摘要
现代经济生活中通货膨胀不可避免,它会对人们的消费-投资、闲暇与自愿退休选择产生影响.文中探讨了经济代理人面对通胀不确定环境如何做出最优消费-组合投资、闲暇和自愿退休选择.代理人的投资机会集包括无风险资产、风险资产和通胀指数债券.用随机微分方程刻画资产价格、通胀水平以及通胀指数债券价格动力学行为,在代理人消费和闲暇预期累计效用最大化目标下,通过动态规划原理,获得关于代理人消费-组合投资、闲暇和自愿退休选择的最优决策闭型解.利用数值模拟分析了通胀波动风险对最优消费和组合投资的影响.发现在低闲暇、高闲暇和退休后三个阶段,代理人面对通胀风险其最优消费-组合投资、闲暇的比重是不同的.
In real economic life,the inflation is inevitable.It would affect an agent's consumption,portfolio,leisure and voluntary retirement.This paper investigates the impact of inflation on the optimalconsumption,portfolio,leisure and voluntary retirement problem for an agent.In addition to investing inriskless assets and risky assets,an agent also invests in the inflation-indexed bond which can be employedto hedge the inflation risk.The dynamics of the stock prices,inflation level and inflation-linked indexbond price are characterized by stochastic differential equations.Under the maximization of expected cu-mulative utility of consumption and leisure,through using dynamic programming principle,the paper de-rived the closed form solutions for an agent's optimal strategy on consumption,portfolio,leisure and re-tirement.Finally,the effects of inflation on the agent's consumption,portfolio and optimal retirement areanalyzed by the numerical simulation.It is also found that an agent's consumption,portfolio and leisureare different during three phases of the agent's lower leisure,higher leisure and retirement.
In real economic life,the inflation is inevitable.It would affect an agent's consumption,portfolio,leisure and voluntary retirement.This paper investigates the impact of inflation on the optimalconsumption,portfolio,leisure and voluntary retirement problem for an agent.In addition to investing inriskless assets and risky assets,an agent also invests in the inflation-indexed bond which can be employedto hedge the inflation risk.The dynamics of the stock prices,inflation level and inflation-linked indexbond price are characterized by stochastic differential equations.Under the maximization of expected cu-mulative utility of consumption and leisure,through using dynamic programming principle,the paper de-rived the closed form solutions for an agent's optimal strategy on consumption,portfolio,leisure and re-tirement.Finally,the effects of inflation on the agent's consumption,portfolio and optimal retirement areanalyzed by the numerical simulation.It is also found that an agent's consumption,portfolio and leisureare different during three phases of the agent's lower leisure,higher leisure and retirement.
引文
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[9]姚海祥,伍慧玲,曾燕.不确定终止时间和通货膨胀影响下风险资产的最优投资策略[J].系统工程理论与实践,2014,34(5):1 089-1 099.
[10]费为银,蔡振球,夏登峰.跳扩散环境下带通胀的最优动态资产配置[J].管理科学学报,2015,18(8):83-94.
[11]J L KOO,B L KOO,Y H SHIN.An optimal investment,consumption,leisure,and voluntary retirement problem with Cobb-Douglas utility:Dynamic programming approaches[J].Applied Mathematics Letters,2013,26(4):481-486.
[12]陈雅豪,梅春晖,费为银.通胀不确定下的最优消费、投资和自愿退休选择[J]安徽工程大学学报,2018,33(2):86-94.
[2]Z BODIE,R C MERTON,W F SAMUELSON.Labor supply flexibility and portfolio choice in a life cycle model[J].Journal of Economic Dynamics and Control,1992,16(3):427-449.
[3]K J CHOI,G SHIM.Disutility,optimal retirement,and portfolio selection[J].Mathematical Finance,2006,16(5):443-467.
[4]E BARUCCI,D MARAZZINA.Optimal investment,stochastic labor income and retirement[J].Applied Mathematics and Computation,2012,218(11):5 588-5 604.
[5]H S LEE,Y H SHIN.An optimal portfolio,consumption-leisure and retirement choice problem with CES utility:a dynamic programming approach[J].Journal of Inequalities&Applications,2015,2015(1):1-13.
[6]C MUNK,C SRENSEN,T NYGAARD VINTHER.Dynamic asset allocation under mean-reverting returns,stochastic interest rates,and inflation uncertainty:Are popular recommendations consistent with rational behavior?[J].International Review of Economics&Finance,2004,13(2):141-166.
[7]A BENSOUSSAN,J KEPPO,S P SETHI.Optimal consumption and portfolio decisions with partially observed real prices[J].Mathematical Finance,2009,19(2):215-236.
[8]M KWAK,B H LIM.Optimal portfolio selection with life insurance under inflation risk[J].Journal of Banking&Finance,2014,46(3):59-71.
[9]姚海祥,伍慧玲,曾燕.不确定终止时间和通货膨胀影响下风险资产的最优投资策略[J].系统工程理论与实践,2014,34(5):1 089-1 099.
[10]费为银,蔡振球,夏登峰.跳扩散环境下带通胀的最优动态资产配置[J].管理科学学报,2015,18(8):83-94.
[11]J L KOO,B L KOO,Y H SHIN.An optimal investment,consumption,leisure,and voluntary retirement problem with Cobb-Douglas utility:Dynamic programming approaches[J].Applied Mathematics Letters,2013,26(4):481-486.
[12]陈雅豪,梅春晖,费为银.通胀不确定下的最优消费、投资和自愿退休选择[J]安徽工程大学学报,2018,33(2):86-94.