Markowitz Portfolio Optimization Extended Quadratic Mean-Field Games Approach.

In this paper, we study the Markowitz dynamic portfolio problem, where individual agents seek to maximize their expected return while minimizing the variance of the return (risk). We model a market with a large number of similar risk-averse agents. For the first time, we incorporate the impact of the agents' aggregated trades using the extended mean-field games framework. We illustrate our results with simmulations.