FBSDEs in a domination-monotonicity framework

报告题目： FBSDEs in a domination-monotonicity framework

报告人：  于志勇教授

报告时间：2021年6月21日16：00

报告地点：数学学院A302

报告人简介：于志勇教授现为山东大学数学学院博士生导师，概率论与数理统计研究所所长。2008年，山东大学数学学院概率论与数理统计专业博士毕业，师从彭实戈院士。2008--2009年应国际著名金融数学专家Jeanblanc教授邀请，赴法国Evry大学概率与金融分析实验室从事博士后研究。2019年入选山东大学杰出中青年学者。2021年获得教育部高等学校科学研究优秀成果（科学技术）二等奖（独立）。于志勇的研究方向为随机最优控制与随机微分博弈、正倒向随机微分方程，和金融数学。在SIAM Journal on Control and Optimization、Science China--Mathematics、ESAIM: Control, Optimisation and Calculus of Variations、Stochastic Processes and their Applications、IEEE Transactions on Automatic Control、Automatica等学术期刊上发表论文30余篇。

报告摘要：  Inspired by various stochastic linear-quadratic (LQ, for short) problems, we develop the method of continuation to study nonlinear forward-backward stochastic differential equations (FBSDEs, for short) in a kind of domination-monotonicity frameworks. The coupling of FBSDEs is in a general form, i.e., it not only appears in integral terms and terminal terms, but also in initial terms. By virtue of introducing various matrices, matrix-valued random variables and matrix-valued stochastic processes, we present the domination-monotonicity framework carefully and rigorously. A unique solvability result and a pair of estimates for coupled FBSDEs are obtained in the case of simple domination-monotonicity conditions and multi-level self-similar domination-monotonicity structures. As applications of theoretical results, the related stochastic Hamiltonian systems of several LQ problems are discussed.

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