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

ShengJun Fan and Long Jiang

Statistics & Probability Letters, 2012, vol. 82, issue 10, 1792-1798

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.

Keywords: Backward stochastic differential equation; Existence; Linear-growth generator; Comparison theorem; Levi type theorem (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spl.2012.06.004

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