Optimal portfolio with relative performance and partial information: A mean‐field game approach

Abstract

AbstractWe use a mean‐field game (MFG) formulation to investigate a family of portfolio management problems with relative performance in a partially observable financial market. The stock price process is characterized by a factor model and investors can only observe past stock price data. All investors share a common investment period and have constant absolute risk aversion (CARA) utility functions. We construct explicit linear feedback equilibria for both a finite population game and a corresponding MFG. Filtering theory and dynamic programming method are involved to solve two kinds of optimization problems with partial information. Our results show that the limiting strategy for ‐agent game can be derived as equilibrium of suitable MFG in a partially observable financial market.