Some uniqueness results for one-dimensional BSDEs with uniformly continuous coefficients

Guangyan Jia

Statistics & Probability Letters, 2009, vol. 79, issue 4, 436-441

Abstract: In this note we discuss one-dimensional backward stochastic differential equations (BSDEs) with coefficient g which is uniformly continuous in (y,z). As we know, the solution to this kind of BSDE may be non-unique. We prove that, the set of real numbers c such that the solution of perturbed BSDE with coefficient g+c is non-unique, is at most countable, and we give some necessary and sufficient conditions for the uniqueness for solution to this kind of BSDEs. More importantly, we prove that if g is independent of y, the solution of corresponding BSDE is unique.

Date: 2009
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