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Portfolio selection under Partial Information and relative performance concerns

We establish a Nash equilibrium in a market with N agents with CARA utility and relative performance criteria, when model paramater is partially observed. Each investor has a Gaussian prior belief on the return rate of the risky asset. The prior belief can be heterogeneous. We characterize the optimal investment strategy for stochastic return rate by a FBSDE. We solve the FBSDEs using a deep learning method and demonstrate the efficiency and accuracy by comparing with the numerical solution from PDE for linear filter case. We find that while investors trade more aggressively under relative performance, the effect is mitigated by partial information.