Multi-dimensional Backward Stochastic Differential Equations of Diagonally Quadratic Generators with a Special Structure

Abstract

The present paper is devoted to the well-posedness of a type of multi-dimensional backward stochastic differential equations (BSDEs) with a diagonally quadratic generator. We give a new priori estimate, and prove that the BSDE admits a unique solution on a given interval when the generator has a sufficient small growth of the off-diagonal elements (i.e., for each \(i\), the \(i\)-th component of the generator has a small growth of the \(j\)-th row \(z^j\) of the variable \(z\) for each \(j \neq i\)). Finally, we give a solvability result when the diagonally quadratic generator is triangular.