On Approximation of the BSDE with Unknown Volatility in Forward Equation

On Approximation of the BSDE with Unknown Volatility in Forward Equation

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We consider the problem of the construction of the backward stochastic differential equation in the Markovian case. We suppose that the forward equation has a diffusion coefficient depending on some unknown parameter. We propose an estimator of this parameter constructed by the discrete time observ...

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Main Authors: Samvel Gasparyan, Yury Kutoyants
Format: Article
Language:English
Published: Republic of Armenia National Academy of Sciences 2015-05-01
Series:Armenian Journal of Mathematics
Online Access:http://test.armjmath.sci.am/index.php/ajm/article/view/111
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spelling doaj-2b06b36f906947b4a15832bccd1557cc2020-11-24T22:32:42ZengRepublic of Armenia National Academy of SciencesArmenian Journal of Mathematics1829-11632015-05-0171On Approximation of the BSDE with Unknown Volatility in Forward EquationSamvel Gasparyan0Yury Kutoyants1Yerevan State University Alex Manoogian, 0025 Yerevan, ArmeniaUniversit´e du Maine Avenue Olivier Messiaen - 72085 Le Mans Cedex 9, France We consider the problem of the construction of the backward stochastic differential equation in the Markovian case. We suppose that the forward equation has a diffusion coefficient depending on some unknown parameter. We propose an estimator of this parameter constructed by the discrete time observations of the forward equation and then we use this estimator for approximation of the solution of the backward equation. The question of asymptotic optimality of this approximation is also discussed. http://test.armjmath.sci.am/index.php/ajm/article/view/111
collection DOAJ
language English
format Article
sources DOAJ
author Samvel Gasparyan
Yury Kutoyants
spellingShingle Samvel Gasparyan
Yury Kutoyants
On Approximation of the BSDE with Unknown Volatility in Forward Equation
Armenian Journal of Mathematics
author_facet Samvel Gasparyan
Yury Kutoyants
author_sort Samvel Gasparyan
title On Approximation of the BSDE with Unknown Volatility in Forward Equation
title_short On Approximation of the BSDE with Unknown Volatility in Forward Equation
title_full On Approximation of the BSDE with Unknown Volatility in Forward Equation
title_fullStr On Approximation of the BSDE with Unknown Volatility in Forward Equation
title_full_unstemmed On Approximation of the BSDE with Unknown Volatility in Forward Equation
title_sort on approximation of the bsde with unknown volatility in forward equation
publisher Republic of Armenia National Academy of Sciences
series Armenian Journal of Mathematics
issn 1829-1163
publishDate 2015-05-01
description We consider the problem of the construction of the backward stochastic differential equation in the Markovian case. We suppose that the forward equation has a diffusion coefficient depending on some unknown parameter. We propose an estimator of this parameter constructed by the discrete time observations of the forward equation and then we use this estimator for approximation of the solution of the backward equation. The question of asymptotic optimality of this approximation is also discussed.
url http://test.armjmath.sci.am/index.php/ajm/article/view/111
work_keys_str_mv AT samvelgasparyan onapproximationofthebsdewithunknownvolatilityinforwardequation
AT yurykutoyants onapproximationofthebsdewithunknownvolatilityinforwardequation
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