This paper studies the optimal investment, consumption and life insurance purchase problem for a wage earner under the condition that the return on the risky asset is predictable. We assume that the market price of risk is an affine function consisting of an observable and an unobservable factor that follow the O-U processes, while the evolution of the interest rate is described by the Vasicek model. The optimal investment, consumption and life insurance strategies and the corresponding value function are derived by adopting the filtering technique and the dynamical programming principle approach. In addition, for comparative analysis, the suboptimal strategies and the utility losses are presented when the wage earner ignores learning or the randomness of the interest rate. Finally, some numerical examples are presented to illustrate the results.

本文研究了在风险资产收益可预测的情况下，工薪阶层的最优投资、消费和寿险购买问题。我们假设风险的市场价格是由遵循OU过程的可观察和不可观察因素组成的仿射函数，而利率的演变由Vasicek模型描述。采用过滤技术和动态规划原理方法推导出最优的投资、消费和寿险策略及相应的价值函数。此外，为了进行比较分析，还提出了当工薪阶层忽视学习或利率随机性时的次优策略和效用损失。最后，给出了一些数值例子来说明结果。