On approximation of BSDE and multi-step MLE-processes

Yu A. Kutoyants

doi:10.1186/s41546-016-0005-0

Article Contents

2016, Volume 1: 4. Doi: 10.1186/s41546-016-0005-0

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On approximation of BSDE and multi-step MLE-processes

Yu A. Kutoyants^,

Laboratoire Manceau des Mathématiques, Université du Maine Le Mans, France and National Research University “MPEI”, Moscow, Russia

Yu A. Kutoyants, kutoyants@univ-lemans.fr

Received: January 2016

Revised: June 14, 2016

Published: September 2020

This work was done with partial financial support of the RSF grant number 14-49-10079.

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Abstract

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.

Keywords:

Backward stochastic differential equation,
Parameter estimation,
Multi-step MLE-process,
Small noise,
Black and Scholes model.

Mathematics Subject Classification: 62M05.

Citation:

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