Existence, uniqueness and stability of backward stochastic differential equations with locally monotone coefficient

Abstract

We prove existence, uniqueness and stability of the solution for multidimensional backward stochastic differential equations (BSDE) with locally monotone coefficient. This is done with an almost quadratic growth coefficient and a square integrable terminal data. The coefficient could be neither locally Lipschitz in the variable y nor in the variable z. To cite this article: K. Bahlali et al., C. R. Acad. Sci. Paris, Ser. I 335 (2002) 757–762.