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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 thedistance between two agents' decisions, we introduce the average deviation. Weformulate the stochastic optimal control problem considering herd behavior andderive the analytical solution through the variational method. We theoreticallyanalyze the impact of users' herd behavior on the optimal decision bydecomposing it into their rational decisions, which is called the rationaldecision decomposition. Furthermore, to quantify the preference for theirrational decision over that of the other agent, we introduce the agent'sinvestment opinion. Our study is validated through simulations on real stockdata.

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