Existence of solutions to one-dimensional BSDEs with semi-linear growth and general growth generators

This paper is devoted to solving a one-dimensional backward stochastic differential equation (BSDE in short) when the generator g has a semi-linear growth and a general growth in (y, z). This condition is not only strictly weaker than the linear growth condition of g in (y, z), but also the (weak) monotonicity and general growth condition of g in y together with the linear growth condition of g in z. We establish, in this setting, three existence results on a solution and the minimal (maximal) solution to the BSDE, where the generator g may be discontinuous in y. These results virtually unify and improve some existing results. (c) 2015 Elsevier B.V. All rights reserved.