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On the existence and uniqueness of solutions to FBSDEs in a non-degenerate case

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  • Delarue, François

Abstract

We prove a result of existence and uniqueness of solutions to forward-backward stochastic differential equations, with non-degeneracy of the diffusion matrix and boundedness of the coefficients as functions of x as main assumptions. This result is proved in two steps. The first part studies the problem of existence and uniqueness over a small enough time duration, whereas the second one explains, by using the connection with quasi-linear parabolic system of PDEs, how we can deduce, from this local result, the existence and uniqueness of a solution over an arbitrarily prescribed time duration. Improving this method, we obtain a result of existence and uniqueness of classical solutions to non-degenerate quasi-linear parabolic systems of PDEs. This approach relaxes the regularity assumptions required on the coefficients by the Four-Step scheme.

Suggested Citation

  • Delarue, François, 2002. "On the existence and uniqueness of solutions to FBSDEs in a non-degenerate case," Stochastic Processes and their Applications, Elsevier, vol. 99(2), pages 209-286, June.
    • Handle: RePEc:eee:spapps:v:99:y:2002:i:2:p:209-286
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    References listed on IDEAS

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    1. Hu, Ying & Yong, Jiongmin, 2000. "Forward-backward stochastic differential equations with nonsmooth coefficients," Stochastic Processes and their Applications, Elsevier, vol. 87(1), pages 93-106, May.
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