Article2006

The wellposedness of FBSDEs

47 citations0/0 files storedDiscrete and Continuous Dynamical Systems - B

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Stochastic processes and financial applications Nonlinear Differential Equations Analysis Fuzzy Systems and Optimization

Abstract

In this paper we investigate the wellposedness of a class of Forward-Backward SDEs. Compared to the existing methods in the literature, our result has the following features: (i) arbitrary time duration; (ii) random coefficients; (iii) (possibly) degenerate forward diffusion; and (iv) no monotonicity condition. As a trade off, we impose some assumptions on the derivatives of the coefficients. A comparison theorem is also proved under the same conditions. This work is motivated by studying numerical methods for FBSDEs.

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References

1990Adapted solution of a backward stochastic differential equation 1997Backward Stochastic Differential Equations in Finance 2005Backward stochastic differential equations and quasilinear parabolic partial differential equations 1994Solving forward-backward stochastic differential equations explicitly — a four step scheme 2007Forward-Backward Stochastic Differential Equations and their Applications 1999Fully Coupled Forward-Backward Stochastic Differential Equations and Applications to Optimal Control 1995Solution of forward-backward stochastic differential equations 1993Backward-Forward Stochastic Differential Equations

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