摘要
This paper studies an investment and consumption problem with stochastic interest rate,where interest rate is governed by the Vasicek model.The financial market is composed of one riskfree asset and one risky asset,in which stock price dynamics is assumed to be generally correlated with interest rate dynamics.The aim is to maximize expected utility of consumption and terminal wealth in the finite horizon.Legendre transform is used to deal with this investment and consumption problem and the explicit solutions of the optimal investment and consumption strategies with power and logarithm preference are achieved.Finally,the authors add a numerical example to analyze the effect of market parameters on the optimal investment and consumption strategy and provide some economic implications.
This paper studies an investment and consumption problem with stochastic interest rate,where interest rate is governed by the Vasicek model.The financial market is composed of one riskfree asset and one risky asset,in which stock price dynamics is assumed to be generally correlated with interest rate dynamics.The aim is to maximize expected utility of consumption and terminal wealth in the finite horizon.Legendre transform is used to deal with this investment and consumption problem and the explicit solutions of the optimal investment and consumption strategies with power and logarithm preference are achieved.Finally,the authors add a numerical example to analyze the effect of market parameters on the optimal investment and consumption strategy and provide some economic implications.
基金
supported by the Humanities and Social Science Research Youth Foundation of Ministry of Education of China under Grant No.11YJC790006
Center for Research of Regulation and Policy of Zhejiang Province of China under Grant No.13JDGZ03YB
the project of National Statistical Science of China under Grant No.2013LY125
the Higher School Science and Technology Development Foundation of Tianjin of China under Grant No.20100821
关键词
最优投资
勒让德变换
消费
模型
随机利率
金融市场
股票价格
动力学
Dynamic programming investment and consumption Legendre transform the closedform solution the Vasicek model
