Stability of solutions of BSDEs with random terminal time

Issue		ESAIM: PS Volume 10, 2006


Page(s)		141 - 163
DOI		10.1051/ps:2006006
Published online		09 March 2006

ESAIM: P&S, March 2006, Vol. 10, pp. 141-163
DOI: 10.1051/ps:2006006

Stability of solutions of BSDEs with random terminal time

Sandrine Toldo

IRMAR, Université Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex, France; sandrine.toldo@math.univ-rennes1.fr

(Received November 25, 2004. Revised April 10 and June 23, 2005. / Published online: 9 March 2006)

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 $\tau$ , 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 $\tau$ .

Mathematics Subject Classification. 60H10, 60Fxx, 60G40

Key words: Backward Stochastic Differential Equations (BSDE), stability of BSDEs, weak convergence of filtrations, stopping times.

© EDP Sciences, SMAI 2006

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