考虑相对业绩的最优投资选择博弈问题研究

Optimal Portfolio Selection Game Problem with Interacting Agents under Relative Performance Concerns

研究了具有相互作用的两个竞争机构投资者之间的离散时间最优投资选择博弈问题,每个机构投资者都考虑其竞争对手的相对业绩.机构投资者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.机构投资者选择投资组合策略使得期望终端绝对财富和相对财富的效用最大.首先,定义了Nash均衡投资组合选择策略.然后,在机构投资者具有指数效用函数的假设下,得到了Nash均衡投资组合选择策略和值函数的显示表达式,分析了机构投资者之间的竞争对Nash均衡投资组合选择策略的影响.最后,通过数值计算给出了各种情况下Nash均衡投资组合选择策略和值函数与模型主要参数之间的关系.结果表明:机构投资者之间的竞争会影响其对风险的承担,投资机会集对机构投资者的Nash均衡投资组合选择策略和值函数与模型主要参数之间的关系会产生很大的影响.

We study the discrete time optimal portfolio selection game problem between two interacting agents when each agent takes into account his relative performance by comparison with his competitor.Both agents can invest freely in the risk-free asset and only one of the two correlated risky stocks is available to each agent,reflecting asset specialization.Each agent chooses a portfolio strategy to maximize his expected terminal utility of his wealth and the difference between his wealth and that of his competitor.We first characterize explicitly the unique Nash equilibrium portfolio strategies.Furthermore,the Nash equilibrium portfolio strategy and the value function of each agent are obtained in closed forms for the case of each agent with an exponential utility function.The effects of the relative performance on the Nash equilibrium portfolio strategy and the value function are also analyzed.Finally,numerical examples are provided to illustrate how the Nash equilibrium portfolio strategy and the value function change when some model parameters vary.The results reveal that competition can change the agent risk taking.Different investment possibilities may greatly influence the Nash equilibrium portfolio strategy and the value function of the agent.