Suppose $N$ is a compact Riemannian manifold, in this paper we will introduce the definition of $N$-valued BSDE and $L^2(\mathbb{T}^m;N)$-valued BSDE for which the solution are not necessarily staying in only one local coordinate. Moreover, the global existence of a solution to $L^2(\mathbb{T}^m;N)$-valued BSDE will be proved without any convexity condition on $N$.
Robustness of quadratic hedging strategies in finance via backward stochastic differential equations with jumps
On backward stochastic differential equations and strict local martingales
Asymptotic behavior of Wasserstein distance for weighted empirical measures of diffusion processes on compact Riemannian manifolds
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