基于通胀的最优投资-消费、闲暇和自愿退休问题  被引量:2

Optimal Investment-Consumption,Leisure and Voluntary Retirement Problem under Inflation

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作  者:恽珍 费为银 梁勇 YUN Zhen;FEI Weiyin;LIANG Yong(School of Mathematics and Physics,Anhui Polytechnic University,Wuhu 241000,China)

机构地区:[1]安徽工程大学数理学院,安徽芜湖241000

出  处:《东华大学学报(自然科学版)》2018年第5期829-838,共10页Journal of Donghua University(Natural Science)

基  金:国家自然科学基金资助项目(71571001)

摘  要:考察通胀环境对一个带有Cobb-Douglas效用函数的代理人的最优投资-消费、闲暇和自愿退休的影响。用通胀对代理人的财富过程进行折现,推导出了财富过程的动力学方程;将代理人生命周期分为低闲暇、高闲暇和退休后3个阶段,获得值函数的解析解和关于投资消费、闲暇和退休的最优决策明确表达式;结合数值模拟,分析了财富水平和通胀不确定因素对消费和投资的影响。结果表明:消费和投资均随着财富水平的增加而增加;通胀的不确定性对消费和投资的影响在每个阶段存在不同的趋势。The impacts of inflation were studied on an optimal investment-consumption, leisureand voluntary retirement problem for an agent with a Cobb-Douglas utility function. The wealth process was discounted and corresponding dynamic equation of the wealth process was derived. The life cycle of agent was divided into three stages : lower leisure, higher leisure and retirement. The closed form solutions were derived for the value function and explicit expressions of optimal strategies for investment consumption, leisure and retirement. The effects of wealth level and inflation uncertainty on the agent's consumption and portfolio were analyzed by the numerical simulation. The results show that both consumption and investment are increasing with respect to the wealth level. The impacts of inflation uncertainty on consumption and investment are different at every stage.

关 键 词:通胀 投资-消费和闲暇 自愿退休 Cobb-Douglas效用 动态规划法 

分 类 号:O211.63[理学—概率论与数理统计] F830.9[理学—数学]

 

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