CAJ | 학술논문

本文在连续时间模型假设下，研究股票价格波动率具有模型不确定对投资者的最优消费和投资策略的影响。首先在股票价格波动率具有模型不确定的条件下，建立最优消费与投资问题的随机控制数学模型，得到了最优消费与投资所满足的HJB方程，并在常相对风险厌恶效用的情形下，获得了最优化问题值函数的显式解。其次当波动率具有模型不确定时，得到了含糊厌恶的投资者是基于股价波动率的上界作出决策的结论，并给出了投资者的最优投资和消费与含糊对冲需求。最后在给定参数的条件下，对所得结果进行了数值模拟和经济分析。
본문재련속시간모형가설하，연구고표개격파동솔구유모형불학정대투자자적최우소비화투자책략적영향。수선재고표개격파동솔구유모형불학정적조건하，건립최우소비여투자문제적수궤공제수학모형，득도료최우소비여투자소만족적HJB방정，병재상상대풍험염악효용적정형하，획득료최우화문제치함수적현식해。기차당파동솔구유모형불학정시，득도료함호염악적투자자시기우고개파동솔적상계작출결책적결론，병급출료투자자적최우투자화소비여함호대충수구。최후재급정삼수적조건하，대소득결과진행료수치모의화경제분석。
This paper studies the effect of the model uncertainty of stock price volatility on an investor’s optimal consumption and portfolio with a continuous-time model. Firstly, a sto-chastic optimal control model for the optimal consumption and investment decision problem is established under the condition of the model uncertainty of stock price volatility. Secondly, through the HJB equation of the optimal consumption and portfolio, an explicit expression of the valued function of the optimization problem in the case of constant relative risk-aversion (CRRA) utility is achieved. Thirdly, we get that the decision-making of an ambiguity averse investor is based on the upper bound of the stock price volatility uncertainty, and discuss the investor’s optimal portfolio and ambiguity hedge demands. Finally, by the numerical simulation the economic analysis of the results is provided.