The Annals of Probability

Existence, uniqueness and comparisons for BSDEs in general spaces

Samuel N. Cohen and Robert J. Elliott

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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.

Article information

Source
Ann. Probab., Volume 40, Number 5 (2012), 2264-2297.

Dates
First available in Project Euclid: 8 October 2012

Permanent link to this document
https://projecteuclid.org/euclid.aop/1349703322

Digital Object Identifier
doi:10.1214/11-AOP679

Mathematical Reviews number (MathSciNet)
MR3025717

Zentralblatt MATH identifier
1260.60128

Subjects
Primary: 60H20: Stochastic integral equations
Secondary: 60H10: Stochastic ordinary differential equations [See also 34F05] 91B16: Utility theory

Keywords
BSDE comparison theorem general filtration separable probability space Grönwall inequality nonlinear expectation

Citation

Cohen, Samuel N.; Elliott, Robert J. Existence, uniqueness and comparisons for BSDEs in general spaces. Ann. Probab. 40 (2012), no. 5, 2264--2297. doi:10.1214/11-AOP679. https://projecteuclid.org/euclid.aop/1349703322


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