基于相对财富效用的多阶段投资组合博弈模型

现有投资组合优化模型普遍假设投资者之间是相互独立的,然而在实际投资过程中投资者往往是相互影响的,尤其是对于机构投资者而言,考虑这种相互影响显得尤为重要。本文基于多阶段投资组合理论和纳什均衡思想,考虑投资者决策之间的影响关系,以每个投资者自身终端相对财富的期望效用水平最大化为目标,构建了多阶段投资组合博弈模型,并给出了纳什均衡投资策略和相应值函数的解析解。最后,采用累计经验分布函数和确定性等价等指标,对纳什均衡投资策略与传统策略进行了比较,结果表明纳什均衡策略更具优越性。

Multi-period Portfolio Game Model Based on Relative Wealth Utility

Most existing portfolio optimization models assume that investors are independent. However, the investors especially institutional investors, usually affect each other in actual investment. Based on the portfolio optimization and Nash game theories, the competition relationship is considered into investors' decision-making, and a multi-period portfolio game model is constructed by maximizing the expected utility of the relative terminal wealth of each competitor. The close forms of the Nash equilibrium investment strategy and the corresponding value function are obtained. By using the empirical cumulative distribution function and the certainty equivalent, the Nash equilibrium investment strategy is compared with the traditional strategy in our simulations. The results show that the Nash equilibrium strategy is more effective for investors.