中文摘要：

基于完备的金融市场条件假设的前提下,当随机利率服从CIR（Cox-Ingersoll-Ross）模型时,研究了带有随机劳动收入的最优消费投资问题.首先,利用Ιto∧公式以及动态规划原理,建立相应的HJB方程并推导出最优的消费投资策略.其次,在幂效用的特殊情形下,给出了相应值函数的显式解以及相应的最优消费和投资决策的显式解.最后,给定相关参数,利用Matlab软件对得到的结果进行数值模拟,同时分析了劳动收入不确定以及风险厌恶程度对最优消费和投资比率的影响,并给出了相应的经济意义解释.

英文摘要：

Based on the complete financial market,the optimal consumption and portfolio with the stochastic labor income are studied when the stochastic interest rate is supposed to be driven by CIR（CoxIngersoll-Ross）model.Firstly,the corresponding HJB equation and the optimal consumption and portfolio strategies are established by using the formula ofΙto∧and the dynamic programming principle.Then,under the power utility,the explicit solution of the value function and the explicit solutions of the optimal consumption and portfolio strategies are derived.Finally,some relative parameters are given and the effect of uncertainty of stochastic labor income and the risk aversion on optimal consumption and portfolio ratio are analyzed by numerical simulation,then the economic significance is explained as well.