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May 2007 Backward stochastic differential equations with random stopping time and singular final condition
A. Popier
Ann. Probab. 35(3): 1071-1117 (May 2007). DOI: 10.1214/009117906000000746

Abstract

In this paper we are concerned with one-dimensional backward stochastic differential equations (BSDE in short) of the following type:

Yt=ξtττYr|Yr|qdrtττZrdBr, t≥0,

where τ is a stopping time, q is a positive constant and ξ is a ℱτ-measurable random variable such that P(ξ=+∞)>0. We study the link between these BSDE and the Dirichlet problem on a domain D⊂ℝd and with boundary condition g, with g=+∞ on a set of positive Lebesgue measure.

We also extend our results for more general BSDE.

Citation

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A. Popier. "Backward stochastic differential equations with random stopping time and singular final condition." Ann. Probab. 35 (3) 1071 - 1117, May 2007. https://doi.org/10.1214/009117906000000746

Information

Published: May 2007
First available in Project Euclid: 10 May 2007

zbMATH: 1125.60054
MathSciNet: MR2319716
Digital Object Identifier: 10.1214/009117906000000746

Subjects:
Primary: 35J60 , 35J65 , 49L25 , 60G40 , 60H10

Keywords: Backward SDE , nonintegrable data

Rights: Copyright © 2007 Institute of Mathematical Statistics

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Vol.35 • No. 3 • May 2007
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