Please use this identifier to cite or link to this item: http://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
RMID: 0020122404
DOI: 10.1214/11-AOP679
Appears in Collections:Statistics publications

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