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September 2012 Existence, uniqueness and comparisons for BSDEs in general spaces
Samuel N. Cohen, Robert J. Elliott
Ann. Probab. 40(5): 2264-2297 (September 2012). DOI: 10.1214/11-AOP679

Abstract

We present a theory of backward stochastic differential equations in continuous time with an arbitrary filtered probability space. No assumptions are made regarding the left continuity of the filtration, of the predictable quadratic variations of martingales or of the measure integrating the driver. We present conditions for existence and uniqueness of square-integrable solutions, using Lipschitz continuity of the driver. These conditions unite the requirements for existence in continuous and discrete time and allow discrete processes to be embedded with continuous ones. We also present conditions for a comparison theorem and hence construct time consistent nonlinear expectations in these general spaces.

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Samuel N. Cohen. Robert J. Elliott. "Existence, uniqueness and comparisons for BSDEs in general spaces." Ann. Probab. 40 (5) 2264 - 2297, September 2012. https://doi.org/10.1214/11-AOP679

Information

Published: September 2012
First available in Project Euclid: 8 October 2012

zbMATH: 1260.60128
MathSciNet: MR3025717
Digital Object Identifier: 10.1214/11-AOP679

Subjects:
Primary: 60H20
Secondary: 60H10 , 91B16

Keywords: BSDE , Comparison theorem , general filtration , Grönwall inequality , nonlinear expectation , separable probability space

Rights: Copyright © 2012 Institute of Mathematical Statistics

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Vol.40 • No. 5 • September 2012
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