Herd Behavior in Optimal Investment: A Dual-Agent Approach with Investment Opinion and Rational Decision Decomposition

In this paper, we study the optimal investment problem involving two agents, where the decision of one agent is influenced by the other. To measure the distance between two agents' decisions, we introduce the average deviation. We formulate the stochastic optimal control problem considering herd behavior and derive the analytical solution through the variational method. We theoretically analyze the impact of users' herd behavior on the optimal decision by decomposing it into their rational decisions, which is called the rational decision decomposition. Furthermore, to quantify the preference for their rational decision over that of the other agent, we introduce the agent's investment opinion. Our study is validated through simulations on real stock data.