时 间：2021年3月19日(周五) 9:00-10:00
地 点：腾讯会议ID：106 769 488
主讲人：孟庆欣 湖州师范学院教授
主讲题目：Global adapted solution of backward stochastic Riccati equations with jump, with application to the mean-variance hedging
摘 要：
In this paper, we investigate the solvability of matrix valued backward stochastic Riccati equations with jumps (BSREJ), which is associated with a stochastic linear quadratic (SLQ) optimal control problem with random coefficients and driven by both Brownian motion and Poisson process. By dynamic programming principle, Doob-Meyer decomposition and inverse flow technique, the existence and uniqueness of the solution for the BSREJ are established. The difficulties addressed to this issue not only are brought from the high nonlinearity of the generator of the BSREJ like the case driven only by Brownian motion, but also from that i) the inverse flow of the controlled linear stochastic differential equation driven by Poisson process may not exist without additional technical condition, and ii) how to show that the inverse matrix term involving jump process in the generator is well-defined. Utilizing the structure of the optimal control problem, we overcome these difficulties and establish the existence of the solution. In additional, we show the construction of the optimal feedback control with the help of the Riccati equation and the relation between the solution of Riccati equation and the value function of the SLQ problem, which also implies the uniqueness for BSREJ. As an application, a mean-variance hedging is discussed.
报告人简介：
孟庆欣， 教授、浙江省杰出青年基金项目获得者、“南太湖本土高层次人才特殊支持计划”科技创新领军人才、浙江省高校中青年学科带头人、湖州市1112人才工程入选者、复旦大学物理系出站博士后。孟庆欣教授一直从事随机分析、随机控制、金融工程等方面的研究工作；主持并完成国家自然科学基金项目3项，在研国家自然科学基金1项，主持并完成省自然科学基金面上项目2项、省杰青项目1项，主持并完成中国博士后特别资助项目和博士后面上项目各一项。孟庆欣近年来先后在《SIAM Journal On Control And Optimization》、《Automatica》、《System & Control Letters》、《Applied Mathematics & Optimization》、《Journal of Computational and Applied Mathematics》、《Journal of Mathematical Analysis and Applications》、《Stochastic Analysis and Applications》、《Applied Mathematics: A Journal of Chinese Universities》、《Journal of Control Theory and Applications》、《中国科学A辑：数学》、《中国科学F辑：信息科学》、《数学年刊》等国内外著名期刊上发表了多篇有关随机控制及其金融工程应用的学术论文，并解决了随机控制理论中的两个重要公开问题，并获得湖州师范学院第三届科研成果奖一等奖1项和湖州师范学院第五届“陆增镛教师奖”。