Existence, uniqueness and comparisons for BSDEs in general spaces

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.

Published in at http://dx.doi.org/10.1214/11-AOP679 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (3)

• A general theory of Finite State Backward Stochastic Difference Equations
• Comparisons for backward stochastic differential equations on Markov chains and related no-arbitrage conditions
• Dynamically Consistent Nonlinear Evaluations and Expectations

Cited by in corpus (4)

• Existence and uniqueness results for BSDEs with jumps: the whole nine yards
• Reflected BSDEs on Filtered Probability Spaces
• Nonlinear reserving and multiple contract modifications in life insurance
• Reflections on BSDEs