Optimal portfolio with relative performance and CRRA risk preferences in a partially observable financial market.

We study a class of optimal portfolio problems with relative performance and constant relative risk aversion (CRRA) risk preferences in a partially observable financial market. The price of a stock is described by a factor model and agents (investors or fund managers) make use of stock price data to estimate the factor process. All agents have CRRA (power or logarithmic) utility functions and they all want to maximize their utilities of above-average wealth and average wealth is the geometric mean of the overall wealth. We use a competition weight to control the tradeoff between absolute and relative performance. We consider both an n -agent game and the corresponding mean field game (MFG). For the finite population game, we give a linear feedback Nash equilibrium. For the MFG, we obtain a linear feedback mean field equilibrium (MFE). Our results show that the limiting strategy for the finite population game can be derived as equilibrium of suitable MFG for CRRA case in a partially observable financial market. • We build two novel models, the n-agent game model and the mean field game model, for competitive optimal portfolio problems with partial information. • We clear up two kinds of optimization problems with partial information by virtue of state decoupling and measure change. • We gain the linear feedback Nash equilibria for the n-agent game and the mean field game. [ABSTRACT FROM AUTHOR]