Abstract
The focus is on the approximation of the solution of BSDE in the case where the solution of forward equation is observed in the presence of small Gaussian noise. The volatility of the forward equation is considered to depend on some unknown parameter. This approximation is made in several steps. First a preliminary estimator of the unknown volatility is obtained, then using Kalman-Bucy filtration equations and Fisher-score device one-step MLE-process of this parameter is constructed. The solution of BSDE is approximated by means of the solution of PDE and the One-step MLE-process. The error of approximation is described in different metrics.
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