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Newton-Kantorovitch method for decoupled forward-backward stochastic differential equations
Dai Taguchi, Takahiro Tsuchiya · 2018-06-05 · via math.PR updates on arXiv.org

We present and prove a Newton-Kantorovitch method for solving decoupled forward-backward stochastic differential equations (FBSDEs) involving smooth coefficients with uniformly bounded derivatives. As Newton's method is required a suitable initial condition to converge, we show that such initial conditions are solutions of a linear backward stochastic differential equation. In addition, we show that converges linearly to the solution.

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