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

François Delarue

Stochastic Processes and their Applications, 2002, vol. 99, issue 2, 209-286

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.

Keywords: Existence; and; uniqueness; Forward-backward; stochastic; differential; equations; Gradient; estimate; Quasi-linear; equations; of; parabolic; type (search for similar items in EconPapers)
Date: 2002
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Handle: RePEc:eee:spapps:v:99:y:2002:i:2:p:209-286