Existence and Comparisons for BSDEs in general spaces

Details Existence and Comparisons for BSDEs in general spaces Existence and Comparisons for BSDEs in general spaces

2010-01-04

arxiv.org/abs/1001.0439v1

Mathematics

Probability

29 pages

Scientific paper

We present a theory of Backward Stochastic Differential Equations in continuous time with an arbitrary filtered probability space. No assumptions are made regarding the continuity of the filtration, or of the predictable quadratic variations of martingales in this space. 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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