论文标题
平均现场投资组合与消费
Mean Field Portfolio Games with Consumption
论文作者
论文摘要
我们研究了使用消费的平均现场投资组合游戏。对于一般市场参数，我们在游戏的NASH平衡与某些FBSDE的解决方案之间建立了一对一的对应关系，事实证明，这与某些BSDE相当。我们的方法足以涵盖权力，指数和日志公用事业，依赖于[3,9]中的Martingale最佳原理和[6,7]中的动态编程原理。当市场参数不取决于布朗路径时，我们将获得封闭形式的唯一NASH平衡。作为副产品，当所有市场参数均与时间无关时，我们回答[12]中提出的问题：[12]中获得的强平衡在本质上是界限的空间中是独一无二的。
We study mean field portfolio games with consumption. For general market parameters, we establish a one-to-one correspondence between Nash equilibria of the game and solutions to some FBSDE, which is proved to be equivalent to some BSDE. Our approach, which is general enough to cover power, exponential and log utilities, relies on martingale optimality principle in [3,9] and dynamic programming principle in [6,7]. When the market parameters do not depend on the Brownian paths, we get the unique Nash equilibrium in closed form. As a byproduct, when all market parameters are time-independent, we answer the question proposed in [12]: the strong equilibrium obtained in [12] is unique in the essentially bounded space.
