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Backward-forward SDE's and stochastic differential games

Author

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  • Hamadène, S.

Abstract

In this paper, the first part is concerned with the study of backward-forward stochastic differential equations without the non-degeneracy condition for the forward equation. We show existence and unicity of the solution to such equations under weaker monotonicity assumptions than those of Hu and Peng (1990). In a second part, we apply the results of the first part for studying the problem of existence of open-loop Nash equilibrium points for nonzero sum linear-quadratic stochastic differential games with random coefficients. We show existence, and give their expression, of such points without any limitation of the duration of the game.

Suggested Citation

  • Hamadène, S., 1998. "Backward-forward SDE's and stochastic differential games," Stochastic Processes and their Applications, Elsevier, vol. 77(1), pages 1-15, September.
    • Handle: RePEc:eee:spapps:v:77:y:1998:i:1:p:1-15
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    Cited by:

    1. Mingcan Wang & Xiangjun Wang, 2024. "Hybrid Neural Networks for Solving Fully Coupled, High-Dimensional Forward–Backward Stochastic Differential Equations," Mathematics, MDPI, vol. 12(7), pages 1-22, April.
    2. Nie, Tianyang & Rutkowski, Marek, 2014. "Multi-player stopping games with redistribution of payoffs and BSDEs with oblique reflection," Stochastic Processes and their Applications, Elsevier, vol. 124(8), pages 2672-2698.

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