资产收益序列相依下的多阶段投资博弈模型

现有投资组合优化研究普遍假设投资者之间相互独立,且假定标的资产在不同阶段的收益序列不具相关性.然而在实际投资过程中,投资者往往是相互影响,资产收益序列也存在相依特征.基于多阶段投资组合优化和纳什均衡理论,利用相对绩效来刻画投资者之间的博弈现象,以每个投资者的相对终端财富的期望效用水平为目标,构建多阶段投资组合博弈模型.在资产收益序列相依情形下,给出了纳什均衡投资策略和相应值函数的解析表达式,以及纳什均衡投资策略与传统策略的关系.采用累计经验分布函数和夏普比率等指标,对纳什均衡投资策略与传统策略进行仿真比较,分析了纳什均衡投资策略随投资者反应敏感系数的变化趋势.结果表明:相比于传统的投资策略,当考虑竞争对手的相对绩效时,纳什均衡策略投资者更愿意冒高风险去追求高收益;并且投资者的反应敏感系数越大,其对风险的偏好程度也越高.

Multi-period portfolio game model with serially correlated returns

The existing literature on portfolio optimization generally assumes that investors are independent,and the returns of underlying assets are not correlated among different periods. In reality,however,investors often relate to each other,and the return series always have some dependencies among different time periods.Under the framework of the multi-period portfolio optimization and Nash equilibrium theories,using the relative performance of investors to describe their game behaviors,a multi-period portfolio game model is constructed which maximizes the expected utility of the relative terminal wealth of each investor. With the assumption of correlated return series,the analytical solutions of Nash equilibrium investment strategy and the corresponding value function are derived,and the relationship between the strategies derived from Nash equilibrium and the traditional ones is described. Finally,a simulation analysis of the two investment strategies,by using cumulative empirical distribution function and Sharpe index to compare the performance of the two strategies'' is conducted,and how Nash equilibrium investment strategies change with the different coefficients of the investors'' response sensitivity is analyzed. Results show that,when considering the relative performance of competitors,investors of Nash equilibrium,with respect to traditional investors,are more willing to tolerate higher risks to pursue higher profits,and the greater the response sensitivity coefficients,the higher risk they prefer.