QUADRATIC BSDE WITH L2-TERMINAL DATA: KRYLOV'S ESTIMATE, ITO- KRYLOV'S FORMULA AND EXISTENCE RESULTS

• 成果类型: Article
• 署名作者: Bahlali, Khaled; Eddahbi, M'hamed; Ouknine, Youssef
• 署名单位: Universite de Toulon; Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS); King Saud University; Cadi Ayyad University of Marrakech
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/16-AOP1115
• 发表日期: 2017
• 页码: 2377-2397
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; 2 reflecting barriers; solvability; GROWTH

摘要

We establish a Krylov-type estimate and an Ito-Krylov change of variable formula for the solutions of one-dimensional quadratic backward stochastic differential equations (QBSDEs) with a measurable generator and an arbitrary terminal datum. This allows us to prove various existence and uniqueness results for some classes of QBSDEs with a square integrable terminal condition and sometimes a merely measurable generator. It turns out that neither the existence of exponential moments of the terminal datum nor the continuity of the generator are necessary to the existence and/or uniqueness of solutions. We also establish a comparison theorem for solutions of a particular class of QBSDEs with measurable generator. As a byproduct, we obtain the existence of viscosity solutions for a particular class of quadratic partial differential equations (QPDEs) with a square integrable terminal datum.