Strategic Index Rebalancing: Differential Games, Closed-Loop Equilibrium, and Mean-Field Dynamics

This study focuses on continuous-time multi-asset trading games before and after index rebalancing, constructing subgame perfect Nash equilibria and mean-field equilibria for opportunistic traders with heterogeneous beliefs about future index composition. Numerical results show that the more intense the competition among opportunistic traders, the smoother the price fluctuations around the implementation date; under the premise of fixed average beliefs, increased belief dispersion can raise total trading volume without changing the net positions and price impact of opportunistic traders.