We consider the problem of approximation of the solution of the backward stochastic differential equations in Markovian case. We suppose that the forward equation depends on some unknown finite-dimensional parameter. This approximation is based on the solution of the partial differential equations and multi-step estimator-processes of the unknown parameter. As the model of observations of the forward equation we take a diffusion process with small volatility. First we establish a lower bound on the errors of all approximations and then we propose an approximation which is asymptotically efficient in the sense of this bound. The obtained results are illustrated on the example of the Black and Scholes model.

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关于BSDE和多步MLE过程的逼近

我们考虑了马尔可夫情况下的倒向随机微分方程解的逼近问题。我们假设正向方程取决于一些未知的有限维参数。该近似基于未知参数的偏微分方程和多步估计器过程的解。作为正向方程式的观测模型，我们采用了具有小波动性的扩散过程。首先，我们为所有近似值的误差建立一个下界，然后我们提出一个在这个边界意义上渐近有效的近似值。布莱克和斯科尔斯模型的例子说明了获得的结果。