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Mean-field backward–forward stochastic differential equations and nonzero sum stochastic differential games
Stochastics and Dynamics  (IF0.98),  Pub Date : 2020-12-03, DOI: 10.1142/s0219493721500362
Yinggu Chen, Boualem Djehiche, Said Hamadène

We study a general class of fully coupled backward–forward stochastic differential equations of mean-field type (MF-BFSDE). We derive existence and uniqueness results for such a system under weak monotonicity assumptions and without the non-degeneracy condition on the forward equation. This is achieved by suggesting an implicit approximation scheme that is shown to converge to the solution of the system of MF-BFSDE. We apply these results to derive an explicit form of open-loop Nash equilibrium strategies for nonzero sum mean-field linear-quadratic stochastic differential games with random coefficients. These strategies are valid for any time horizon of the game.