Heston模型下考虑随机劳动收入的最优投资问题

基于Heston随机波动率模型研究投资者拥有一份随机劳动收入的最优投资问题。假设金融市场由一个风险资产（股票）和无风险资产（银行存款）构成，并考虑投资者拥有一份随机劳动收入，在指数效用函数下使其终端财富最大化；利用随机控制方法得到该问题的最优投资策略的解析表达式，通过数值模拟分析模型中的主要参数以及劳动收入对最优投资策略的影响。结果表明：随着投资者的劳动收入波动率增大，投资到风险资产的比例减小；在风险厌恶系数增大时，投资到风险资产的比例也减小；风险资产的投资比例对Heston模型中的参数变化非常敏感。

Optimal Investment Problem of Considered Stochastic Labor Income Under Heston Model

Based on Heston stochastic volatility model, the optimal investment problem of investors with a random labor income is studied. Assume that the financial market consists of a risky asset(stock) and a risk-free asset(bank deposits), and consider that investors have a random labor income to maximize their terminal wealth under the exponential utility function. The stochastic control method is used to obtain the analytical expression of the optimal investment strategy for this problem, and the influence of the main parameters in the model and labor income on the optimal investment strategy is analyzed by numerical simulation. The results show that with the increase of labor income volatility, the proportion of investment in risk assets decreases. When the risk aversion coefficient increases, the proportion of investment in risk assets also decreases. The investment proportion of risk assets is very sensitive to the changes of parameters in Heston model.