The Annals of Probability
- Ann. Probab.
- Volume 40, Number 5 (2012), 2264-2297.
Existence, uniqueness and comparisons for BSDEs in general spaces
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.
Ann. Probab., Volume 40, Number 5 (2012), 2264-2297.
First available in Project Euclid: 8 October 2012
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60H20: Stochastic integral equations
Secondary: 60H10: Stochastic ordinary differential equations [See also 34F05] 91B16: Utility theory
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