Mean-field backward–forward stochastic differential equations and nonzero sum stochastic differential games
Keyword(s):
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.
Linear quadratic stochastic optimal control problems with operator coefficients: open-loop solutions
2019 ◽
Vol 25
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pp. 17
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2016 ◽
Vol 54
(3)
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pp. 1826-1858
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2013 ◽
Vol 51
(4)
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pp. 2809-2838
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2020 ◽
Vol 136
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pp. 104624
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Keyword(s):
Keyword(s):
2017 ◽
Vol 54
(4)
◽
pp. 977-994
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