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Existence, uniqueness and comparisons for BSDEs in general spaces. (English) Zbl 1260.60128

The authors consider backward stochastic differential equations with an arbitrary filtered probability space and without any additional assumptions regarding the left-continuity of the filtration. Predictable quadratic variation of the integrating martingale and the measure that integrates the driver can be arbitrary as well. Existence and uniqueness conditions are established, where the driver is integrated with respect to an arbitrary deterministic Stieltjes measure. A comparison theorem is proved for the solutions. This result shows under which conditions the solutions describe nonlinear expectations and evaluations in the sense of Peng. Time consistent nonlinear expectations are constructed in the general filtered spaces.

MSC:

60H20 Stochastic integral equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
91B16 Utility theory
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