Article2008

A uniqueness theorem for the solution of Backward Stochastic Differential Equations

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Stochastic processes and financial applications Nonlinear Differential Equations Analysis Fuzzy Systems and Optimization

Abstract

In this Note, we prove that if g is uniformly continuous in z , uniformly with respect to ( ω , t ) and independent of y , the solution to the backward stochastic differential equation (BSDE) with generator g , is unique.

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References

1990Adapted solution of a backward stochastic differential equation 2000Backward stochastic differential equations and partial differential equations with quadratic growth 1997Backward stochastic differential equations with continuous coefficient 2002Filtration-consistent nonlinear expectations and related g-expectations 1998Backward Stochastic Differential Equations and Viscosity Solutions of Systems of Semilinear Parabolic and Elliptic PDEs of Second Order 2008Quadratic BSDEs with convex generators and unbounded terminal conditions 1990Stochastic Analysis and Related Topics II

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2018General mean-field BSDEs with continuous coefficients 2010Backward stochastic differential equations with a uniformly continuous generator and related g -expectation 2010One-dimensional BSDEs with finite and infinite time horizons

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