Mean-field backward-forward stochastic differential equations and nonzero sum stochastic differential games

Yinggu Chen; Boualem Djehiche; Said Hamadene

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arXiv · 1904.06193

Mean-field backward-forward stochastic differential equations and nonzero sum stochastic differential games

Yinggu Chen·Boualem Djehiche·Said Hamadene

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Abstract

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.

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BibTeX RIS

Yinggu Chen, Boualem Djehiche, Said Hamadene. 2019-04-12. Mean-field backward-forward stochastic differential equations and nonzero sum stochastic differential games. https://arxiv.org/abs/1904.06193

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