Existence and uniqueness of solutions for bsdes with locally lipschitz coefficient

Abstract

We deal with multidimensional backward stochastic differential equations (BSDE) with locally Lipschitz coefficient in both variables y, z and an only square integrable terminal data. Let LN be the Lipschitz constant of the coe�cient on the ball B(0, N) of Rd × Rdr. We prove that if LN = O(√logN), then the corresponding BSDE has a unique solution. Moreover, the stability of the solution is established under the same assumptions. In the case where the terminal data is bounded, we establish the existence and uniqueness of the solution also when the coe�cient has an arbitrary growth (in y) and without restriction on the behaviour of the Lipschitz constant LN. © 2002 Association for Symbolic Logic.