The Equivalence between Uniqueness and Continuous Dependence of Solution for BSDEs with Continuous Coefficient

TL;DR

This paper proves that for BSDEs with continuous, linearly growing coefficients, the uniqueness of solutions is equivalent to their continuous dependence on the data, linking two fundamental properties.

Contribution

It establishes the equivalence between solution uniqueness and continuous dependence for BSDEs with continuous coefficients, a novel theoretical insight.

Findings

Uniqueness and continuous dependence are equivalent for BSDEs with continuous, linearly growing coefficients.

The result applies to BSDEs with coefficients g(t,y,z) continuous in (y,z).

Provides a theoretical foundation for stability analysis of BSDE solutions.

Abstract

In this paper, we will prove that, if the coefficient $g=g(t,y,z)$ of a BSDE is assumed to be continuous and linear growth in $(y,z)$, then the uniqueness of solution and continuous dependence with respect to $g$ and the terminal value $\xi$ are equivalent.