| Abstract: |
| We study a type of mean field portfolio games with a major and N minor agents with private information, where the major agent is not allowed to trade on the market after a given unpredictable and external default time to the market. The investment horizon of each minor agent is divided into two intervals with and without the major in the market, leading naturally to two sequential optimization problems. Using the martingale optimality principle, a Nash equilibrium of the limiting problem (N\rightarrow\infty) is characterized by a type of coupled multi-dimensional mean-field FBSDEs with quadratic growth and random horizon, which is solvable under a weak interaction assumption of minor agents. The convergency of Nash equilibrium between the limiting problem and the original (N+1) portfolio games is also verified. We study the well-posedness and the stability results of a extended BSDEs with quadratic growth and random horizon in the Appendix. |
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