A uniqueness theorem for the solution of Backward Stochastic Differential Equations

Abstract

In this Note, we prove that if g is uniformly continuous in z , uniformly with respect to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo stretchy="false">(</mml:mo> <mml:mi>ω</mml:mi> <mml:mo>,</mml:mo> <mml:mi>t</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> and independent of y , the solution to the backward stochastic differential equation (BSDE) with generator g , is unique.