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.
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