不完全金融市场下基于二次效用函数的动态资产分配

Dynamic asset allocation based on quadratic utility function in an incomplete financial market

为了研究不完全市场条件下的连续时间动态投资组合选择问题,首先应用降维方法将不完全市场转化为完全市场,然后在转化后的完全市场条件下应用鞅方法得出二次效用函数意义下的最优投资策略.进而应用转化后的完全市场和原不完全市场下各参数的关系得到二次效用意义下不完全市场环境里最优投资策略的解析表达式,并分析风险厌恶因子对最优投资策略的影响.最后为了说明不完全市场和完全市场条件下投资者最优投资策略的变化,给出算例进行分析.

This paper is concerned with continuous-time dynamic portfolio selection problem in an incomplete market.A complete market is created directly from the incomplete one by reducing the dimensions of the underlying Brownian motion.We derive optimal investment strategies based on quadratic utility function in the created complete market applying martingale method.According to the relations between the created complete market and the original incomplete one,we give explicit form solutions of optimal portfolio in the original incomplete market and analyze the effect of risk aversion factor on the optimal portfolio.Finally,the results obtained are illustrated on an example.