One-dimensional BSDEs with left-continuous, lower semi-continuous and linear-growth generators

• DOI: 10.1016/j.spl.2012.06.004
• Publication Date: 2012-06-13T17:28:28Z
• Authors: ShengJun Fan; Long Jiang
• Keywords: Linear growth; Comparison theorem; Uniform continuity; Hölder condition

Abstract This paper deals with a one-dimensional backward stochastic differential equation (BSDE) whose generator g is of linear growth in ( y , z ) , left-continuous and lower semi-continuous (maybe discontinuous) in y , and continuous in z . We establish, in this setting, the existence of the minimal solution to the BSDE. And we also prove a comparison theorem and a Levi type theorem for the minimal solutions. They generalize some known results.