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Stability of solutions of BSDEs with random terminal time

Published online by Cambridge University Press:  09 March 2006

Sandrine Toldo
Sandrine Toldo*
Affiliation:
IRMAR, Université Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex, France; sandrine.toldo@math.univ-rennes1.fr
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Abstract

In this paper, we study the stability of the solutions of Backward Stochastic Differential Equations (BSDE for short) with an almost surely finite random terminal time. More precisely, we are going to show that if (Wn) is a sequence of scaled random walks or a sequence of martingales that converges to a Brownian motion W and if $(\tau^n)$ is a sequence of stopping times that converges to a stopping time τ, then the solution of the BSDE driven by Wn with random terminal time $\tau^n$ converges to the solution of the BSDE driven by W with random terminal time τ.

Keywords

Backward Stochastic Differential Equations (BSDE)stability of BSDEsweak convergence of filtrationsstopping times.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 10 , February 2006 , pp. 141 - 163
Copyright
© EDP Sciences, SMAI, 2006

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