On the robustness of backward stochastic differential equations.
type: Item
instance of: scholarly article
title: On the robustness of backward stochastic differential equations.
zbMATH Open document ID: 1058.60041
DOI: 10.1016/S0304-4149(01)00131-4
author: Philippe Briand
author: Bernard Delyon
author: Jean Mémin
published in: Stochastic Processes and their Applications
publication date: 2005-02-25T00:00:00Z
review text: The backward stochastic differential equation driven by a Brownian motion \(W=\{W_t\} _{0\leq t\leq T}\), \[ Y_t= \xi + \int _t^T f(r,Y_r, Z_r)\,dr -\int _t^T Z_r\,dW_r,\quad 0\leq t\leq T, \] is considered, where the solution \((Y_t, Z_t)\) is supposed to be progressively measurable with respect to the filtration \(\{\mathcal F_t \}\) defined by the Brownian motion [for existence and uniqueness of such solution under suitable conditions see e.g.\ \textit{E. Pardoux} and \textit{S. G. Peng}, Syst. Control Lett. 14, 55--61 (1990; Zbl 0692.93064)]. The main result of the paper is ``robustness'' of solutions: If \((\xi ^n, f^n, W^n)\) converges to \((\xi , f,W)\) in an appropriate sense, the solutions of approximating equations converge to the solution of the limiting one as well. It should be noted that \(W^n\) is not assumed to have the predictable representation property. As a byproduct, the convergence of a ``Euler scheme'' for BSDE is obtained.
Mathematics Subject Classification ID: 60H10
zbMATH DE Number: 2138939
zbMATH Keywords: backward stochastic differential equation
zbMATH Keywords: stability of backward stochastic differential equations
MaRDI profile type: Publication
cites work: Stopping times and tightness. II
cites work: Backward stochastic differential equations and integral-partial differential equations
cites work: Donsker-type theorem for BSDEs
cites work: Q2725614
cites work: Q4086511
cites work: Q3915688
cites work: Q4357500
cites work: Backward Stochastic Differential Equations in Finance
cites work: Calcul stochastique et problèmes de martingales
cites work: Explicit form and robustness of martingale representations.
cites work: On tightness and stopping times
cites work: Q3774629
cites work: Q4895006
cites work: Q3979063
cites work: Adapted solution of a backward stochastic differential equation
cites work: Probabilistic interpretation of a system of semilinear parabolic partial differential equations
cites work: Generalized BSDEs and nonlinear Neumann boundary value problems
cites work: Q3996259
cites work: Q3997782
full work available at URL: s0304-4149(01)00131-4
OpenAlex ID: W2016859865
description: scientific article; zbMATH DE number 2138939