为了研究在随机消费和随机利率情形下，不同因素对最优投资策略的影响，选择基于常数方差弹性(constant elasticity of variance，CEV)模型，并在常数绝对风险厌恶(constant absolute risk aversion，CARA)效用函数下，利用对偶方法、Legendre变换和动态规划原理，得到终端财富期望效用最大化问题的最优投资策略。同时，通过数值模拟说明随机利率、随机消费等参数对最优投资策略的影响。研究结果表明:当风险资产波动率、风险厌恶系数以及利率增加时，投资者会减少股票投资比例;而当股票的平均回报率和现金收入的波动率增加时，投资者会增加股票的投资比例。
Optimal Investment Strategy with Random Consumption and Random Interest Rate Based on CEV Model
To study the impact of different factors on the optimal investment strategy in the case of random consumption and random interest rates,the optimal investment strategy for maximizing the expected utility of terminal wealth is obtained based on the Constant Elasticity of Variance(CEV)model and under the constant absolute risk aversion(CARA)utility function,using the dual method,Legendre transformation and dynamic programming principle.Numerical simulations are conducted to demonstrate the impact of parameters such as random interest rates and random consumption on the optimal investment strategy.The research results show that when the volatility of risk assets,risk aversion coefficient and interest rates increases,investors will tend to reduce their stock investment proportion whereas when the average return on stocks and the volatility of cash income increase,investors will increase the proportion of stock investments.
random interest ratehamilton-jacobi-bellman equationCEV modelCARA utility
万方数据
维普
