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## Control and Optimization seminar

- 9/13

Control And Optimization Seminar

A Class Of Dimensionality-free Metrics For Convergence Of Empirical Measures

Ruimeng Hu (UCSB)

Control And Optimization Seminar

A Class Of Dimensionality-free Metrics For Convergence Of Empirical Measures

Ruimeng Hu (UCSB)

2:00 PM - 3:00 PM

Storrs Campus

OnlineAbstract: This talk concerns the convergence of empirical measures in high dimensions. We propose a new class of metrics and show that under such metrics, the convergence is free of the curse of dimensionality, in contrast to Wasserstein distance. Proposed metrics originate from maximum mean discrepancy, which we generalize by proposing criteria for test function spaces. Examples include RKHS, Barron space, and flow-induced function spaces. Three applications are presented: 1. Convergence of empirical measures for random variables; 2. Convergence of the n-particle system to the McKean-Vlasov SDE; 3. Construct Nash equilibrium for homogeneous n-player game by its mean-field limit. This is joint work with Jiequn Han and Jihao Long.

Webex Meeting link:

https://uconn-cmr.webex.com/uconn-cmr/j.php?MTID=m2575f9f4e5074f3a1e2322381036ae71

Meeting number:

120 570 8973

Password:

UConn

Speaker's bio: Ruimeng 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. Please visit her website for more information: https://sites.google.com/site/ruimenghu1/

Contact Information: Bin Zou, bin.zou@uconn.edu More - 9/27

Control And Optimization Seminar

Monte-Carlo Methods For High-Dimensional Problems In Quantitative Finance

Mete Soner (Princeton)

Control And Optimization Seminar

Monte-Carlo Methods For High-Dimensional Problems In Quantitative Finance

Mete Soner (Princeton)

2:00 PM - 3:00 PM

Storrs Campus

OnlineAbstract: Stochastic optimal control has been an effective tool for many problems in quantitative finance and financial economics. Although, they provide the much needed quantitative modeling for such problems, until recently they have been intractable in high-dimensional settings. However, several recent studies report impressive numerical results: Cheredito, Becker and Jentzen (2019, Journal of Machine Learning Research) studied the optimal stopping problem (a problem closely connected to pricing American type options in quantitative finance finale) providing tight error bounds and an efficient algorithm up to 100 dimensional problems. Buehler, Gonon, Teichmann and Wood (2019, Quantitative Finance) on the other hand, considers the problem of hedging and again reports results for high-dimensional problems that were intractable. All these papers use a Monte-Carlo type algorithm combined with deep neural networks proposed by Han, E and Jentzen. In this talk I will outline this approach and discuss its properties. Numerical results, while validating the power of the method in high dimensions,

also show the dependence of the dimension and the size of the training data. This is joint work with Max Reppen of Boston University and Valentin Tissot-Daguette from Princeton.

Webex Meeting link: https://uconn-cmr.webex.com/uconn-cmr/j.php?MTID=mbf144adcaf1f064d1a9242202b7d9581

Meeting number: 120 535 2896 Password: UConn

Speaker's bio: Mete is a Professor of Operations Research and Financial Engineering at Princeton University. He is also affliated with the Bendheim Center of Finance and with the Program in Applied & Computation Mathematics. Previously, he was a professor of mathematics and the Chair of the department at ETH Zurich. His research is on decisions under uncertainty and I work on related problems in stochastic optimal control, Markov decision processes, nonlinear partial differential equations, probability theory, mathematical finance and financial economics. Please visit his website for more information: https://soner.princeton.edu/

Contact Information: Bin Zou, bin.zou@uconn.edu More - 11/8

Control And Optimization Seminar

Gibbs' Theory And Statistical Physics: A Third Approach To Understanding The World Probabilistically?

Hong Qian (University of Washington)

Control And Optimization Seminar

Gibbs' Theory And Statistical Physics: A Third Approach To Understanding The World Probabilistically?

Hong Qian (University of Washington)

2:00 PM - 3:00 PM

Storrs Campus

onlineAbstract: How to apply the mathematical theory of probability to real world problems? Interpretations of "what is probability" have led to the Bayesian and frequentist schools. In very elementary terms, I try to show how Gibbs' theory stitches together both thoughts, as well as the large deviations theory, an asymptotic analysis of the law of large numbers. This yields the statistical ensemble as a parametric family of probabilistic models that are specifically informed by the nature of "observables". Two well-known entropy functions, Gibbs' and Shannon's, as well as Pitman–Koopman–Darmois theorem, figure prominently in our theory.

Webex Meeting Link: https://uconn-cmr.webex.com/uconn-cmr/j.php?MTID=m1f2ce5d7489c3cc07e239637b5d9677f (Meeting Number: 2620 090 8808 Password: UConn)

Speaker's short bio: Hong Qian is Olga Jung Wan Professor of Applied Mathematics and Adjunct Professor in Bioengineering at the University of Washington. Professor Qian's main research interest is the mathematical approach to and physical understanding of biological systems, especially in terms of stochastic mathematics and nonequilibrium statistical physics. He received his B.A. in Astrophysics from Peking University in China, and his Ph.D. in Biochemistry and Biophysics from Washington University School of Medicine in St. Louis. Please visit his website for more information: http://faculty.washington.edu/hqian/.

Contact Information: Bin Zou, bin.zou@uconn.edu More - 11/15

Control And Optimization Seminar

Duality And Deep Learning For Optimal Consumption With Randomly Terminating Income

Harry Zheng (Imperial College, London)

Control And Optimization Seminar

Duality And Deep Learning For Optimal Consumption With Randomly Terminating Income

Harry Zheng (Imperial College, London)

2:00 PM - 3:00 PM

Storrs Campus

OnlineAbstract: We establish a rigorous duality theory for a problem of optimal consumption in the presence of an income stream that can terminate randomly at an exponentially distributed time, independent of the asset prices. We thus close a duality gap encountered by Davis and Vellekoop (2009) in a version of this problem in a Black-Scholes market. We then solve the problem numerically, using the primal and dual controls, second order BSDEs, and deep learning, to find the optimal control and tight lower and upper bounds for the value function. (Joint work with Ashley Davey and Michael Monoyios).

Webex meeting link: https://uconn-cmr.webex.com/uconn-cmr/j.php?MTID=m64b517c52c22431966ad6cd5da3d108b

(Meeting number: 2624 509 7661 Password: UConn)

Speaker's short bio: Harry is a full professor in the Department of Mathematics at Imperial College London. His research interests include stochastic control and optimization, and financial mathematics. Please visit his website for more information: https://www.ma.imperial.ac.uk/~hz/.

Contact Information: bin.zou@uconn.edu (Bin Zou) More - 11/29

Control And Optimization Seminar

Expert Prediction Problem

Xin Zhang (University Of Vienna)

Control And Optimization Seminar

Expert Prediction Problem

Xin Zhang (University Of Vienna)

2:00 PM - 3:00 PM

Storrs Campus

OnlineAbstract: This talk focuses on expert prediction problem with finite horizon, which is formulated as a zero sum game between a player and an adversary. By considering a scaled game, the value function of discrete games converges to the viscosity solution of a PDE. We explicitly solve this nonlinear PDE with N = 4 experts. By showing that the solution is C^2, we are able to show that the comb strategies, as conjectured in “Towards Optimal Algorithms for Prediction with Expert Advice” by Peres et al., form an asymptotic Nash equilibrium. We also prove the “Finite vs Geometric regret” conjecture proposed in Peres et al. for N = 4, and show that this conjecture in fact follows from the conjecture that the comb strategies are optimal. This talk is based on a joint work with Erhan Bayraktar and Ibrahim Ekren.

Webex meeting link: https://uconn-cmr.webex.com/uconn-cmr/j.php?MTID=m0e001a40b4f4c4e435299d38b02df9e0

Meeting number: 2622 896 7255 Password: UConn

Speaker's short bio: Xin is currently a University Assistant at the University of Vienna. He obtained his Ph.D. from the University of Michigan in 2021. His research interests include probability, stochastic analysis, mean field game, optimal transport, and online learning. Please visit his website for more information: https://sites.google.com/umich.edu/xzhang/home

Contact Information: bin.zou@uconn.edu (Bin Zou) More - 12/6

Control And Optimization Seminar

On Kyle-Back Equilibrium Problem -- The Case Of Dynamic Information

Jin Ma (University Of South California)

Control And Optimization Seminar

On Kyle-Back Equilibrium Problem -- The Case Of Dynamic Information

Jin Ma (University Of South California)

2:00 PM - 3:00 PM

Storrs Campus

OnlineAbstract: We consider the well-known Kyle-Back Strategic Insider Trading problem in the case of dynamic information, that is, we assume that the informed investor (i.e. the insider) is able to observe the liquidity value of the asset dynamically. Assuming that the market price is determined via a Bertrand competition, hence the optional projection of the underlying asset value, we Markovize the problem by introducing an auxiliary diffusion process in the spirit of the weighted total order process, through a set of “pricing rule” functions. By considering a class of stochastic Two-Point Boundary Value Problems (STPBVP), which removes the martingale requirement of the popular dynamic Markov bridge in the literature, we propose a solution scheme for the equilibrium problem under a very general model of the underlying asset. In the case when the solution of STPBVP has an affine structure, we show that the pricing rule functions, whence the Kyle-Back equilibrium, can be determined by the decoupling field of a forward-backward SDE obtained via a non-linear filtering approach. This is a joint work with Ying Tan.

Webex meeting link: https://uconn-cmr.webex.com/uconn-cmr/j.php?MTID=m7427a88ddb186d6e77e6575f7410bebf

Meeting number: 2621 023 6499

Password: UConn

Speaker's short bio: Jin is a full professor at the University of South California and serves as the Director of the Mathematical Finance Program there. Previously he was an assistant/associated/full professor at Purdue University. He obtained his Ph.D. in Mathematics in 1992 from the University of Minnesota. His primary research interests include stochastic analysis, stochastic differential equations, stochastic control theory, mathematical finance, stochastic insurance, and more. Please visit his website https://dornsife.usc.edu/jin-ma/ for more information.

Contact Information: bin.zou@uconn.edu (Bin Zou) More

*Past talks in or after Spring 2020 are accessible through the UConn Events Calendar.*

List of talks prior to Spring 2019.

List of talks prior to Spring 2019.