部分信息下基于过度自信的动态最优消费投资决策

Dynamic Optimal Consumption and Investment Strategy with Incomplete Information Based on Overconfidence

研究了投资者不知道风险资产的收益均值,并在过度自信的影响下,根据观测到的风险资产价格来推测其收益均值的真实值情况下的最优消费投资决策问题.将行为金融理论中过度自信这一重要的认知偏差纳入经典的最优消费投资问题中考虑,建立了部分信息下的最优消费投资决策模型,并运用随机动态规划原理得到了最优消费投资策略.在CRRA效用函数下发现,因风险资产收益均值的未知而导致的投资者套利需求为负,并得到了一个重要的结论:由于金融市场中信息的不完全,投资者过度自信时,其投资于风险资产的绝对值最优比例不一定增大.

An optimal consumption and investment strategy is proposed, in case an investor doesn＇t know the mean return of the risk asset and conjectures the actual mean return in accordance to the risky asset price he observed owing to his influence of overconfidence. Taking the overconfidence as an important cognitive bias into the consideration of classical optimal consumption and investment problem, an optimal consumption and investment model is set up with incomplete information. Then, an optimal consumption and investment strategy is given by use of stochastic dynamic programming theory. For the case of specific CRRA utility, it is shown that the induced hedging demand arising from the ignorance of mean return on the risky assets is negative. An important conclusion is thus drawn that the absolute value of optimal proportion of one＇ s investment in risky assets increases uncertainly for an overconfident investor because of the incomplete information on financial market.