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On Approximation of the BSDE withUnknown Volatility in Forward Equation

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CC BY-NC 4.0 This work is licensed under Creative Commons Attribution–NonCommercial International License (CC BY-NC 4.0).

Abstract

We consider the problem of the construction ofthe backward stochastic differential equation in the Markoviancase. We suppose that the forward equation has a diffusion coef-ficient depending on some unknown parameter. We propose anestimator of this parameter constructed by the discrete time ob-servations of the forward equation and then we use this estimatorfor approximation of the solution of the backward equation. Thequestion of asymptotic optimality of this approximation is alsodiscussed.

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