报告人：薄立军教授

报告时间：5月27日（周 六）上午8:30—9:30

报告地点：统计与数据科学学院213

报告题目：A stochastic control problem arising from relaxed wealth tracking with a monotone benchmark process

报告摘要：We study a nonstandard stochastic control problem motivated by the optimal consumption with wealth tracking of a non-decreasing benchmark process. In particular, the monotone benchmark is modelled by the running maximum of a drifted Brownian motion. We consider a relaxed tracking formulation using capital injection such that the wealth compensated by the injected capital dominates the benchmark process at all times. The stochastic control problem is to maximize the expected utility on consumption deducted by the cost of the capital injection under the dynamic floor constraint. By introducing two auxiliary state processes with reflections, an equivalent auxiliary control problem is formulated and studied such that the singular control of capital injection and the floor constraint can be hidden. To tackle the HJB equation with two Neumann boundary conditions, we establish the existence of a unique classical solution to the dual PDE in a separation form using some novel probabilistic representations involving the dual reflected processes and the local time,  and a homogenization technique of Neumann boundary conditions. The proof of the verification theorem on the optimal feedback control can be carried out by some technical stochastic flow analysis of the dual reflected processes and estimations of the optimal control.

报告人简介：薄立军，教授。本科毕业于西安电子科技大学、硕士和博士毕业于南开大学概率论与数理统计专业，研究方向为随机分析、随机控制与金融数学。先后主持国家自然科学基金青年、面上、中科院前沿科学重点以及陕西国家应用数学中心交叉团队培育项目等。目前已在Ann. Appl. Probab.、Math. Finan.、Stoch. Process. Appl.、SIAM J. Contr. Optim.、SIAM J. Finan. Math.、Math. Opers. Res.、J. Banking Finan.等学术期刊发表学术论文60余篇，出版本科和研究生教材四部。

报告人：邓昌松教授

报告时间：5月27日（周 六）上午9:30—10:30

报告地点：统计与数据科学学院213

报告题目：Finite time blowup of solutions to fractional SPDEs

报告摘要：Finite time blowup in the almost sure sense of a class of space-time fractional SPDEs is discussed. Both the cases of white noise and colored noise are considered. The sufficient and necessary condition between the blowup and Osgood condition is obtained when the spatial domain is bounded. And the sufficient condition for the blowup is obtained when the spatial domain is the whole space.

报告人简介：邓昌松，武汉大学副教授。主要从事随机分析的研究，已在

Trans. AMS, Potential Analysis, Stochastic Process. Appl., Electron. J. Probab. , Adv. in Appl. Probab.等国际学术期刊发表学术论文多篇。

报告人：王汉超教授

报告时间：5月27日（周 六）上午10:30—11:30

报告地点：统计与数据科学学院213

报告题目：Spectral Norm of Products of Random and Deterministic matrices

报告摘要：We study the tail bounds of the spectral norm of matrices $BA$, where $A$ is a random matrix with independent mean zero subexponential entries and $B$ is a fixed matrix. We show that the spectral norm of such an $m\times n$ matrix $BA$ exceeds $\sqrt{n}+\sqrt{m}$ with a exponential decay probability. As an application, we obtain a upper bound for the supremum of the spectral norm by a modified Talagrand's generic chaining method.

报告人简介：山东大学金融研究院教授，博士生导师。主要从事概率统计极限理论及其应用的研究，特别在弱收敛，集中不等式与金融统计等领域发表了若干文章。主持国家自然科学基金两项，作为骨干成员，参加国家重点研发计划项目两项。