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

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:126

Article

Fan, ShengJun¹ 

[1] China Univ Min & Technol, Coll Sci, Nanjing 221116, Jiangsu, Peoples R China

关键词: Backward stochastic differential equation;    Existence and uniqueness;    Comparison theorem;    L-P solution;    Bounded solution;    Infinite time interval;   

DOI  :  10.1016/j.spa.2015.11.012

来源: Elsevier

【 摘 要 】

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, L-P (p > 1) solutions and L-1 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 L-2 solution. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

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