Anticipated backward stochastic differential equations with quadratic growth

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:270

Article

Hu, Ying¹  Li, Xun²  Wen, Jiaqiang³ 

[1] Univ Rennes, CNRS, IRMAR UMR 6625, F-35000 Rennes, France

[2] Hong Kong Polytech Univ, Dept Appl Math, Hong Kong, Peoples R China

[3] Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Guangdong, Peoples R China

关键词: Anticipated backward stochastic differential equation;    Backward stochastic differential equation;    Quadratic generator;    Time-advanced;   

DOI  :  10.1016/j.jde.2020.07.001

来源: Elsevier

【 摘 要 】

In this paper, we study the solvability of anticipated backward stochastic differential equations (BSDEs, for short) with quadratic growth for one-dimensional case and multi-dimensional case. In these BSDEs, the generator f (.), which is of quadratic growth in Z., involves not only the present information of solution (Y, Z.) but also its future one. The existence and uniqueness of such BSDEs, under different conditions, are derived for several terminal situations, including small terminal value, bounded terminal value and unbounded terminal value. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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