Dr. Robert Almgren
Lecturer, ORF 474 Spring 2020
Financial market microstructure, high frequency trading, high frequency data analysis, optimal trade execution, and machine learning methods for all of the above.
Professor Amirali Ahmadi
Room 329, Sherrerd Hall - Ext. 6416
Professor Rene Carmona (On Sabbatical 2020-21)
Room 210, Sherrerd Hall - Ext. 2310
Stochastic analysis, stochastic control and stochastic games, especially mean field games. High Frequency markets, environmental finance and energy and commodity markets.
Professor Matias Cattaneo
Room 227, Sherrerd Hall - Ext. 8825
Econometric theory and mathematical statistics; program evaluation and treatment effects; machine learning, nonparametric and semiparametric methods; high-dimensional inference; applications to social and behavioral sciences.
Professor Jianqing Fan
Room 205, Sherrerd Hall - Ext. 7924
Finance, machine learning, statistics, portfolio choices, financial risks, computational biology, among others.
Junior Independent Work/Senior Thesis Topics:
Professor Boris Hanin (Coming to ORFE September 2020)
Theory of Deep Learning: Neural networks are machine learning models that have achieved state of the art in a variety of practical tasks. I am interested in elucidating the principles by which they work, understanding how to make them better, and extracting the general lessons they hold for statistics and machine learning. A key question is: at finite but large depth and width, what is the statistical behavior of neural networks at initialization? This concerns inductive bias, aligning priors to datasets, and setting hyperparameters such as architecture, learning rate, non-linearity, batch size, etc in a principled way. In addition to such probabilistic/statistical questions, I am also fascinated by understanding the roles of data augmentation and large vs. small learning rates. The questions can involve a range of tools from random matrix theory to combinatorics, the renormalization group, and high dimensional probability.
Semiclassic Analysis: Bohr's correspondence principle says that in the limit of large quantum numbers, quantum mechanics should begin to resemble classical mechanics. For example, by studying a quantum mechanical system in the limit where Planck's constant h tends to zero (the so-called semiclassical limit), the high energy behavior of quantum states should resemble the long-time behavior of the underlying classical system. I am interested in various questions that try to make such claims precise. Usually, they involve studying the zero set and/or density of states for randomized wavefunctions at high frequency/energy. The tools involved range from riemannian geometry to Gaussian processes, geometric measure theory, spectral theory for self-adjoint operators, and special functions.
Random Polynomials: The location and behavior of the zeros of polynomials are a classical topic math and science. It is a famous theorem that for polynomials of degree five and higher in one variable there is no formula for their zeros as a function of their coefficients. Nonetheless, a lot can be said about the zeros of a polynomial when it is chosen at random. For example, a result due to Gauss is that if p_n is a degree n polynomial of one complex variable, then its critical points (solutions to p_n'(z)=0) are inside the convex hull of its zeros. It turns out that much more is true with high probability if p_n is chosen at random. Namely, most of its zeros have a unique nearby critical point. Amazingly, this rather surprising fact was not known until a few years ago, and much remains to be understood! The tools here involve probability and complex analysis.
Dr. Margaret Holen
Lecturer, ORF 473 Spring 2020
As a finance industry practitioner and Goldman Sachs partner, I have extensive project supervision experience related to financial markets and investment banking applications. My current industry focus is on advising and investing in early-stage FinTech companies, with an emphasis on “alternative” data and machine learning. In addition, I am currently teaching an ORFE course focused on FinTech in consumer lending, which explores how evolving data sets and ML toolkits are changing that sector, and I have interest in a variety of related research topics.
Current senior thesis topics under supervision (’18-’19) include:
Professor Jason Klusowski (Coming to ORFE September 2020)
I am broadly interested in the theory and application of various statistical learning models, in particular tree-structured models (e.g., random forests, gradient tree boosting, CART), neural networks, statistical network models, and latent variable models.
Professor Alain L. Kornhauser
Room 229, Sherrerd Hall - Ext. 4657
Development and application of operations research and other analytical techniques in various aspects of Autonomous Vehicles, aka "SmartDrivingCars", including:
Junior Independent Work/Senior Thesis Topics: Any of the above.
Professor William A. Massey (On Sabbatical 2020-21)
Room 206, Sherrerd Hall - Ext. 7384
The applications of and theory for the dynamics of resource sharing. Motivating examples include the design and management of communication networks as well as healthcare systems. Research interests are in dynamic rate queueing theory, stochastic networks, dynamical systems, optimal control, Monte-Carlo simulation, and time-inhomogeneous Markov processes.
Professor John M. Mulvey
Room 207 Sherrerd Hall – Ext. 5423
Large-scale stochastic optimization models, algorithms, and applications, especially financial planning and wealth management. Multi-period financial planning applications for large insurance companies, hedge funds, global FinTech firms, and individuals. Apply novel methods in machine learning to financial planning systems. Combining advanced mathematical financial models with deep neural networks to address transaction costs and overcome the exponential growth in model size.
Conducting research with Ant Financial (Alibaba) on enterprise risk management for a global FinTech firm, and several large banks in San Francisco and New York City, and a multi-manager hedge fund in Austin Texas.
Junior Independent Work/Senior Thesis Topics:
Professor Miklos Racz
Room 204, Sherrerd Hall - Ext. 8281
My research focuses on probability, statistics, and its applications. I am interested in statistical inference problems in complex systems, in particular on random graphs and in genomics. I am also interested more broadly in applied probability, combinatorial statistics, information theory, control theory, interacting particle systems, and voting.
Professor Mykhaylo Shkolnikov
Room 202, Sherrerd Hall - Ext. 1044
Professor Ronnie Sircar
Room 208, Sherrerd Hall - Ext. 2841
Financial Mathematics & Engineering; stochastic models, especially for market volatility; optimal investment and hedging strategies; analysis of financial data; credit risk; dynamic game theory and oligopoly models; energy and commodities markets; reliability of the electricity grid under increased use of solar and wind technologies.
Professor Mete Soner
Room 225, Sherrerd Hall, Ext.- 5130
Mathematical theory of optimal control and decisions under uncertainty, and applications of stochastic optimization techniques in economics, financial economics and quantitative finance, and high-dimensional computational problems. Current topics are:
Professor Bartolomeo Stellato (Coming to ORFE September 2020)
Development of theory and data-driven computational tools for mathematical optimization, machine learning and optimal control. Applications include control of fast dynamical systems, finance, robotics and autonomous vehicles. Mathematical optimization - Large-scale and embedded convex optimization - First-order methods for sparse, low-rank and combinatorial optimization - Differentiable optimization Machine learning for optimization - Learning heuristics to accelerate combinatorial optimization algorithms - Learning solutions of optimization problems with varying data Control systems - Learning control policies for continuous and hybrid systems - High-speed online optimization for real-time control
Professor Ludovic Tangpi
Room 203 Sherrerd Hall – Ext. 4558
My research interests are in stochastic calculus and mathematical finance. More specifically, my work in stochastic analysis aims at developing the understanding of stochastic control and stochastic differential games using probabilistic arguments. Such control and differential games arise in a variety of optimal decision applications, including optimal investment, economics, engineering or biology. Some of the main issues here concern the analysis of optimal decision policies in diffusion models, the study of representations that enable their efficient numerical computations, and similar questions for games with a large number of players.
In mathematical finance, I focus on developing the theory of quantitative risk management. Here, I put a particular emphasis on computational aspects, and develop tools needed to achieve efficient computation. In fact, financial agents (especially banks and insurance companies) are eager to evaluate the riskiness of their decision and often evaluate associated risks periodically. Therefore, it is essential to understand computational issues: When using a particular model, how to select it? Can we use the specificities of a particular model to improve the estimation? How do we account for model uncertainty? It is possible to build model-free methods? Or statistical estimations entirely data-driven? Can we derive theoretical guarantees and convergence rates? This line of work includes (and is not limited to) elements of probability theory, stochastic calculus, as well a numerical and data analysis.
Professor Robert J. Vanderbei
Room 209, Sherrerd Hall - Ext. 0876
Large-scale mathematical optimization models arising in engineering and corresponding solution methodologies.
Junior Independent Work/Senior Thesis Topics
Professor Ramon van Handel
Room 207, Fine Hall – Ext. 3791
I am broadly interested in probability theory and its interactions with other fields. Probability theory, i.e., the study of randomness, is a very rich subject: it combines many different types of mathematics, and is used to solve a surprisingly diverse range of problems in different fields. I am particularly fascinated by the development of probabilistic principles and methods that explain the common structure in a variety of pure and applied mathematical problems.