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https://hdl.handle.net/2440/74759
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Type: | Journal article |
Title: | Existence, uniqueness and comparisons for BSDEs in general spaces |
Author: | Cohen, S. Elliott, R. |
Citation: | Annals of Probability, 2012; 40(5):2264-2297 |
Publisher: | Inst Mathematical Statistics |
Issue Date: | 2012 |
ISSN: | 0091-1798 |
Statement of Responsibility: | Samuel N. Cohen and Robert J. Elliott |
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. |
Keywords: | BSDE comparison theorem general filtration separable probability space Grönwall inequality nonlinear expectation |
Rights: | 2012 © Institute of Mathematical Statistics |
DOI: | 10.1214/11-AOP679 |
Grant ID: | ARC |
Published version: | http://dx.doi.org/10.1214/11-aop679 |
Appears in Collections: | Aurora harvest 4 Statistics publications |
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