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<北京大学数量经济与数理金融教育部重点实验室>学术报告——Special Session on Financial Mathematics

2022-05-12 9:00-11:00 Zoom

 

Title: Some topics on reachability, policy iteration and strategic learning in (stochastic) control problems

Abstract: In this talk, I will describe one of my current projects, which is motivated from (backward) reachability in path planning/robot control and is related to strategic learning in the context of machine learning. One interesting aspect is the policy iteration algorithm in the continuous time setting. There will be more open problems than proved results in this talk.

Bio: Wenpin Tang is currently an Assistant Professor in the Department of IEOR at Columbia University. He graduated from the Department of Statistics at UC Berkeley, and previously worked at the Department of Mathematics at UCLA. He was the recipient of the Prize for Excellence in Financial Markets from Morgan Stanley in 2017. Wenpin Tang works at the intersection of stochastic analysis, machine learning and quantitative finance. His current research interest is to improve the efficiency of machine learning algorithms using stochastic tools, and to develop robust AI methodology for the emerging fintech market. 

 

Title: Convergence of Empirical Measures, Mean-Field Games, and Deep Learning Algorithms

Abstract: In this talk, we first propose a new class of metrics and show that under such metrics, the convergence of empirical measures in high dimensions is free of the curse of dimensionality, in contrast to Wasserstein distance. Proposed metrics originate from the maximum mean discrepancy, which we generalize by proposing criteria for test function spaces. Examples include RKHS, Barron space, and flow-induced function spaces. One application studies the construction of Nash equilibrium for the homogeneous n-player game by its mean-field limit (mean-field game). Another application is to show the ability to overcome curves of dimensionality of deep learning algorithms, for example, in solving Mckean-Vlasov forward-backward stochastic differential equations with general distribution dependence. The is joint work with Jiequn Han and Jihao Long.

Bio: Ruimeng Hu is an Assistant Professor at the University of California, Santa Barbara, with a joint appointment in Mathematics and Statistics and Applied Probability. Before that, she worked at Columbia University as a Term Assistant Professor. Her current research interests lie in the interdisciplinary area of machine learning, financial mathematics, and game theory. She is supported by an NSF grant and Faculty Career Development Award, Regents' Junior Faculty Fellowship at UCSB. 

 

Title: Reinforcement Learning in Finance: Introduction and Survey

Abstract: This talk aims to introduce the basics of reinforcement learning (RL) and review its financial applications. In an RL framework, an intelligent agent learns to make and improve her decisions by interacting with the unknown environment, and by observing her state trajectories and a sequence of reward signals. RL provides a natural setting for decision-making problems where there are fewer assumptions needed on the underlying models. This talk starts with the introduction on Markov decision processes (MDP) which is the setting for many of the commonly used algorithms.  Several popular RL algorithms will then be covered with details. Finally, we discuss the applications of these RL approaches in a variety of decision-making problems in finance including optimal execution, portfolio optimization, market making, and robo-advising.
This talk is based on a survey paper with Ben Hambly and Huining Yang (https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3971071

Bio: Renyuan Xu is currently a WiSE Gabilan Assistant Professor in the Epstein Department of Industrial and Systems Engineering at the University of Southern California. Before joining USC, she spent two years as a Hooke Research Fellow in the Mathematical Institute at the University of Oxford mentored by Professor Rama Cont. She completed her Ph.D. in IEOR Department at UC Berkeley under the supervision of Professor Xin Guo in 2019. Her research interests lie broadly in the span of mathematical finance, stochastic analysis, game theory, and machine learning.

 

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