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发布时间:2023-05-15文章来源: 浏览次数:


报告时间:527日(周 六)上午8:309:30


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.

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。


报告时间:527日(周 六)上午9:3010:30


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.


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。


报告时间:527日(周 六)上午10:3011:30


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.


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