On Approximation of the BSDE withUnknown Volatility in Forward Equation

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On Approximation of the BSDE withUnknown Volatility in Forward Equation Samvel Gasparyan

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.

DOI: https://armjmath.sci.am/index.php/ajm/article/view/111 Armenian Journal of Mathematics, 7(1) 59-79

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Keywords

Backward SDE, approximation of the solution, volatility esti-mation.

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