Bounded solutions, Lp(p>1) solutions and L1 solutions for one dimensional BSDEs under general assumptions

ShengJun Fan

Stochastic Processes and their Applications, 2016, vol. 126, issue 5, 1511-1552

Abstract: This paper aims at solving one dimensional backward stochastic differential equations (BSDEs) under weaker assumptions. We establish general existence, uniqueness, and comparison results for bounded solutions, Lp(p>1) solutions and L1 solutions of the BSDEs. The time horizon is allowed to be finite or infinite, and the generator g is allowed to have a general growth in y and a quadratic growth in z. As compensation, the generator g needs to satisfy a kind of one-sided linear or super-linear growth condition in y, instead of the monotonicity condition in y as is usually done. Many of our results improve considerably some known results, even though for the case of finite time horizon and the case of L2 solution.

Keywords: Backward stochastic differential equation; Existence and uniqueness; Comparison theorem; Lp solution; Bounded solution; Infinite time interval (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:126:y:2016:i:5:p:1511-1552

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DOI: 10.1016/j.spa.2015.11.012

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