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

ShengJun Fan

Statistics & Probability Letters, 2016, vol. 109, issue C, 7-15

Abstract: 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.

Keywords: Backward stochastic differential equation; Semi-linear growth; General growth; Existence; Minimal solution (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1016/j.spl.2015.10.012

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