\Abstract{文章研究了两个风险厌恶的投资者之间的离散时间多期合作投资选择博弈问题. 两个投资者都可以投资于相同的无风险资产和不同的具有相关关系的风险股票, 以反映投资的资产专门化. 首先, 构建了两个投资者之间的合作投资选择博弈模型, 并定义了Nash均衡投资策略. 其次, 在风险股票的收益率服从正态分布和投资者具有指数效用函数下, 得到了Nash均衡投资策略和值函数的显示表达式. 最后, 分析了投资者之间的合作对Nash均衡投资策略和值函数的影响, 得到了两个投资者都具有效用收益的条件, 探讨了Nash均衡投资策略和效用损益与模型主要参数之间的关系, 并给出相应的经济分析. 研究发现, 当风险股票收益率之间负相关或相互独立时, 合作条件下投资者投资于风险股票的资金会超过不合作时投资于风险股票的资金, 投资者之间的合作投资会改变其对风险的承担. 投资者之间是否能稳定合作依赖于投资者对风险的态度和金融市场参数, 当风险股票收益率之间相互独立时, 只有当两个投资者在初始时刻的相对风险厌恶系数之比在0.5和2之间时, 投资者之间进行合作投资才能够增加双方的终端期望财富效用.

In this paper we study a discrete time multi-period cooperative portfolio selection game problems between two risk-averse investors. Both investors can invest freely in the risk-free asset and only one of the two correlated risky stocks is available to each investor, reflecting asset specialization. We first set up a cooperative portfolio selection game model between two investors, and characterize explicitly the unique Nash equilibrium portfolio policies. Secondly, the Nash equilibrium portfolio policies and the value function of each investor are obtained in closed forms for the case of each investor with an exponential utility function and the returns of the two risky stocks are normally distributed. Finally, the effects of the cooperation on the Nash equilibrium portfolio policies and the value functions are also analyzed. We derive sufficient conditions under which the two investors have a utility gain. We also give the corresponding economic analysis. Sensitivity analysis is provided to illustrate how the Nash equilibrium portfolio policies and the utility loss or gain change when some model parameters vary. The investor will increase her equilibrium risky investments relative to the normal case of no cooperation when the correlation parameter between two risky stock returns is negative or zero. The results reveal that cooperation can change the investor risk taking. Whether investors can take cooperative depends on investors' attitude to risk and financial market parameters. If two risky stock returns are independent, then the cooperation can increase the expected terminal wealth utilities of the two investors when the relative risk aversion parameter of the two investors at the initial time is between 0.5 and 2.