Optimal Investment With Incomplete Information and Herd Effect

Due to incomplete information in financial markets, asset returns and volatility are generally not observable to normal investors. To address this issue, normal investors can use historical price data to estimate these parameters. In this process, they often exhibit bounded rationality, demonstrating their limited cognitive and information-processing capabilities. Also, given the investment expertise of experts, normal investors can refer to and align with the experts’ decisions, which is called the herd effect. To better understand normal investors’ behaviors, in this work, we modify the general market parameter estimation methods and propose sliding window-based estimation methods to model their bounded rationality. We then formulate the optimal investment problem, which involves one expert and one normal investor whose decisions are influenced by the expert, and jointly consider incomplete information and the herd effect. We derive the analytical solution for the normal investor’s optimal decision and theoretically analyze the influence of bounded rationality, incomplete information, and herd effect on his/her decisions. We validate our analysis using numerical experiments on real data.