This will be an in-person seminar talk.

Abstract: We consider an infinite horizon optimal investment and consumption problem for an agent who invests in a Black-Scholes market and is unwilling to consume below a fixed proportion of her consumption habit. We consider two cases for the habit process. In one, it is the running maximum of past consumption rates and, in the other, it is the exponentially weighted average. In both cases, the optimal investment and consumption policies are obtained semi-explicitly and in terms of the solutions of nonlinear free-boundary problems, which we analyze in detail. This is joint work with Erhan Bayraktar and Virginia Young.

Speaker's short bio: Bahman is an assistant professor at the University of Miami. Prior to the current position, he was a postdoc at the University of Washington and at the University of Michigan. He obtained his DPhil in Mathematics from the University of Oxford in 2014 under the supervision of Thaleia Zariphopoulou. Please visit his website https://bahmanang.github.io/ for more information.

This is an in-person seminar at MONT 214.

Abstract: In this talk, I will introduce a new class of deep neural network-based numerical algorithms for nonlinear filtering named deep filter. It presents a computationally feasible procedure for regime-switching diffusions. In lieu of the traditional conditional-distribution-based filtering that suffers from curse of dimensionality, we convert it to a problem in a finite-dimensional setting to approximate the optimal weights of a neural network. Then we construct a stochastic gradient-type procedure to approximate these weight parameters, and develop another recursion for adaptively approximating the optimal learning rate. We show the convergence of the combined algorithm using stochastic averaging and martingale methods. Finally, I will talk about the filtering with degenerate observation noise using stochastic approximation approach. Several examples will be presented to show the robustness of the algorithm. This is based on joint work with George Yin and Qing Zhang.

Speaker's short bio: Hongjiang is a PhD student at UConn Math, supervised by Prof. George Yin. His research interests include stochastic control and optimization, and their interface with machine learning.

Please join this online seminar via the Webex link:
https://uconn-cmr.webex.com/uconn-cmr/j.php?MTID=mf7032f9c249bc2d9ea8ccc2241ce072d

(Meeting number: 2623 009 1631 Password: neM36Sq2rBK)

Abstract: In this talk, we first review some recent results on two-stage stochastic
variational inequalities (SVIs). Next we discuss dynamic stochastic variational
inequalities (DSVIs) with uncertainties in dynamic variational inequalities
(DVIs), which include two-stage SVIs as a special case. We show the existence and uniqueness of a solution for a class of DSVIs and the convergence of the
sample average approximation (SAA) of the DSVI. A time-stepping EDIIS method is proposed to solve the DVI arising from the SAA of DSVI.

Speaker's short bio: Dr. Chen is a Chair Professor in the Department of Applied Mathematics at Hong Kong Polytechnic University. She is an elected fellow of SIAM and AMS, and was the department chair from 2013 to 2019. Her research interests include stochastic equilibrium problems, Iterative methods for nonlinear/singular/nonsmooth equations, complementarity problems and applications, nonsmooth, nonconvex optimization, verification methods, and Spherical t-designs. She has published over 100 articles and is an associate editor of various journals. Please visit her website https://www.polyu.edu.hk/ama/staff/xjchen/ChenXJ.htm for more information.

Webex meeting link:
https://uconn-cmr.webex.com/uconn-cmr/j.php?MTID=m38bd90ff9eb2fc69aebf604906dffab7

(Meeting number: 2621 936 4394
Password: JRrzpxPr457)

Abstract: This work studies the deep learning-based numerical algorithms for optimal hedging problems in markets with general convex transaction costs. Our main focus is on how these algorithms scale with the length of the trading time horizon. Based on the comparison results of the FBSDE solver by Han, Jentzen, and E (2018) and the Deep Hedging algorithm by Buehler, Gonon, Teichmann, and Wood (2019), we propose a Stable-Transfer Hedging (ST-Hedging) algorithm, to aggregate the convenience of the leading-order approximation formulas and the accuracy of the deep learning-based algorithms. Our ST-Hedging algorithm achieves the same state-of-the-art performance in short and moderately long traging horizon as FBSDE solver and Deep Hedging, and generalize well to long time horizon when previous algorithms become suboptimal. With the transfer learning technique, ST-Hedging drastically reduce the training time, and shows great scalability to high-dimensional settings. This opens up new possibilities in model-based deep learning algorithms in economics, finance, and operational research, which takes advantage of the domain expert knowledge and the accuracy of the learning-based methods.

Speaker's short bio: Xiaofei is an Assistant Professor in the Department of Statistical Sciences at the University of Toronto. Before joining U of T, she worked as a Term Assistant Professor at Columbia University. She obtained her PhD in Mathematical Finance at Carnegie Mellon University, under the supervision of Prof. Johannes Muhle-Karbe. Her research interests include stochastic optimization, stochastic differential equations with applications to mathematical finance, and more recently data science (such as crowdsourcing, dimensionality reduction, and sparse recovery). Please visit her website https://xf-shi.github.io/ for more information.