MAFN Faculty
Ph.D., Princeton University, 2023
Stochastic Processes – Applications I
MBA, Analytic Finance, University of Chicago, 1998
Multi-Asset Portfolio Management
Irina Bogacheva is Director of Research at Millburn Ridgefield and Adjunct Professor within the Department of Mathematics.
Previously, she held senior research positions with Goldman Sachs, Deutsche Asset Management, QS Investors, and Franklin Templeton. Irina’s professional experience includes research and implementation of systematic global macro strategies, strategic and dynamic asset allocation, and active factor equity strategies. She holds Diploma in Mathematics from Moscow State University, Master’s in Economics from New Economic School (Moscow), and an MBA in Analytic Finance from the University of Chicago Booth School of Business, where she also completed Ph.D. coursework in Finance.
MA, Mathematics of Finance, Columbia University, 2012
Introduction to Quantitative Balance Sheet Strategy (QBSS) for Commercial Banks
Greg Borovykh is a Managing Director at JPMorganChase’s Treasury and Chief Investment Office (TCIO). In this role, he leads a research team responsible for quantitative risk and resource allocation which includes investment portfolio strategy, balance sheet optimization and banking industry surveillance.
Greg is CFA charterholder; he earned BBA in Accounting and Economics from Baruch College and MA in Mathematics of Finance from Columbia University.
Adjunct Professor, Department of Mathematics
MS, Columbia University
Quantitative Methods in Investment Management
Alberto Botter is a Managing Director within the Portfolio Management department at AQR Capital Management. In this role, he oversees the construction, optimization, and management of AQR’s Equities Long-Short and Tax-Managed portfolios. Prior to AQR, Mr. Botter was a quant in the Wealth Strategies Group at Morgan Stanley. Alberto earned a B.S. and an M.S. in economics from the University of Bologna and an M.A. in Mathematics of Finance from Columbia University.
Adjunct Professor, Department of Mathematics
Ph.D., International School for Advanced Studies
Credit Models, Computational Finance, and Machine Learning
Luca is the Global Head of Quantitative Strategies (QS) Credit at Credit Suisse, where he has worked since 2004. Previous to this role, he was the global head of QS for Credit and Structured Notes; he was the EMEA head and the US head of QS Global Credit Products; he worked in Commodities in New York and London, and he was part of the cross-asset modeling R&D group of QS in the London office.
Luca is also Visiting Professor at the Department of Mathematics at University College London, and an Adjunct Professor at Columbia University. His current research interests are in Credit Models, Computational Finance, and Machine Learning, with a focus on efficient numerical techniques for Derivatives Pricing and Risk Management, and applications of Adjoint Algorithmic Differentiation (AAD), which he has pioneered in Finance and Physics, and for which he holds a US Patent. Luca has published over 70 scientific papers, with the top 3 papers collecting to date over 1000 citations (h factor 27, i10 factor 49).
Prior to working in Finance, Luca was a researcher at the Kavli Institute for Theoretical Physics, Santa Barbara, California, working in High-Temperature Superconductivity and Quantum Monte Carlo methods for Condensed Matter systems. He has been awarded the Director’s fellowship at Los Alamos National Laboratory, and the Wigner Fellowship at Oak Ridge National Laboratory.
Luca holds an M.S. cum laude in Physics from the University of Florence, and an M.Phil. and a Ph.D. cum laude in Condensed Matter Theory, from the International School for Advanced Studies, Trieste.
PhD, Princeton University, 1995
Capital Markets and Investments, Math Methods in Financial Price Analysis
Alexei Chekhlov is an Adjunct Assistant Professor within the Department of Mathematics. He has previously taught graduate courses such as “Mathematical Methods in Financial Price Analysis” and “Capital Markets and Investments.” Additionally, Chekhlov serves as the Head of Research and Partner at Systematic Alpha Management, LLC, and he previously worked as a research associate at Princeton University, where he conducted research on the theory of fluid turbulence. He has published repeatedly on fluid mechanics, the kinetic theory of gases, turbulence, and within the fields of applied mathematics and quantitative finance. Chekhlov earned his Ph.D. in Applied and Computational Mathematics from Princeton University.
PhD, University of Valladolid (Spain) and the University of Toulouse III (France), 2023
Statistical Inference / Time-Series Modelling
Alberto González Sanz is an Assistant Professor in the Department of Statistics, with research interests in optimal transport, statistics, artificial intelligence, probability theory, and partial differential equations. He completed his PhD through a cotutelle program between the University of Valladolid (Spain) and the University of Toulouse III (France) in 2023.
MSc, Ecole Polytechnique, 2015
MSc, Corps des Mines, 2018
Interest Rates Models
Paul-Guillaume Fournié has been working as an Options Rates Quant at BNP Paribas’ New York office since 2019, heading the team locally since 2022. Covering both Vanilla and Exotic options, his most recent focus has been on the creation and adaptation of interest rates models to SOFR. He holds MSc in Mathematics and Physics from Ecole Polytechnique and MSc in Economics and Public Policy from Corps des Mines. Before switching to finance he occupied several positions in leading French industrial and telecommunications companies and served in France’s Ministry of the Economy.
Adjunct Professor, Department of Mathematics
PhD, Columbia University, 1996
Numerical Methods in Finance and Risk Model Methodologies
Tat Sang Fung is an Adjunct Professor at Columbia University, and he currently teaches “Numerical Methods in Finances,” a graduate course required for students in the Mathematics of Finance program. His areas of expertise include Quantitative Finance and Risk Management Methodology, and Mathematics. Additionally, Fung serves as the Global Head of Risk Model Methodology at Jefferies and has held other senior positions in the finance industry at Finch Lead Inc. and Finastra. Fung earned his Ph.D. in Mathematics from Columbia University.
fts@math.columbia.edu | 212-854-5880 | Website
Adjunct Professor, Department of Mathematics
PhD, École des ponts ParisTech, 2006
Nonlinear Option Pricing
Julien Guyon is a professor of Applied Mathematics at Ecole des Ponts ParisTech, one of the oldest and one of the most prestigious French Grandes Ecoles, where he holds the BNP Paribas Chair Futures of Quantitative Finance. Before joining Ecole des Ponts, Julien worked in the financial industry for 16 years, first in the Global Markets Quantitative Research team at Societe Generale in Paris (2006-2012), then as a senior quantitative analyst in the Quantitative Research group at Bloomberg L.P., New York (2012-2022). Julien was also an adjunct professor in the Department of Mathematics at Columbia University and at the Courant Institute of Mathematical Sciences, NYU, from 2015 to 2022; and previously at Universite Paris Diderot and Ecole des Ponts ParisTech. Julien serves as an Associate Editor of Finance & Stochastics, SIAM Journal on Financial Mathematics, Quantitative Finance, and Journal of Dynamics and Games. He is also a Louis Bachelier Fellow.
Julien co-authored the book Nonlinear Option Pricing (Chapman & Hall, 2014) with Pierre Henry-Labordere. He has published more than 20 articles in peer-reviewed journals (including Finance and Stochastics, SIAM Journal on Financial Mathematics, Quantitative Finance, Risk, Journal of Computational Finance, Annals of Applied Probability, Stochastic Processes and their Applications) and is a regular speaker at international conferences, both academic and professional. His main research interests include volatility and correlation modeling, option pricing, optimal transport, and numerical probabilistic methods.
A big soccer fan, Julien has also published articles on fairness in sports both in academic journals and in top-tier newspapers including The New York Times, The Times, Le Monde, and El Pais. Some of his suggestions for draws and tournament design have been adopted by FIFA and UEFA, including a new, fairer draw method for the FIFA World Cup; a fairer format for the 2026 FIFA World Cup (in progress); a new knockout bracket for the UEFA Euro; and an optimized schedule of the UEFA Champions League. His paper “Risk of collusion: Will groups of 3 ruin the FIFA World Cup?” won the 2nd prize at the 2021 MIT Sloan Sports Analytics Conference, the biggest sports analytics event in the world.
PhD, Columbia University, 1980
Probability, Stochastic Control, Mathematical Economics, and Finance
Ioannis Karatzas is the Eugene Higgins Professor of Applied Probability in Columbia’s Department of Mathematics, whose research interests include Probability and Mathematical Statistics, Random Processes, Stochastic Analysis, Optimization, and Mathematical Economics and Finance. He has served as the managing editor for the book series Applications of Mathematics and on numerous editorial boards such as “Applied Mathematics & Optimization,” “Stochastics,” the “SIAM Journal on Mathematical Analysis,” and the “SIAM Journal on Control & Optimization.” His book with Steven Shreve, Brownian Motion and Stochastic Calculus, first published in 1987, is the standard reference within the field of Stochastic Analysis. Karatzas earned his Ph.D. from Columbia University and helped build and establish this Mathematics of Finance Master’s program.
Adjunct Professor, Department of Mathematics
PhD, University of Waterloo, 1995
Credit analytics, Risk Management, FinTech
David X. Li currently teaches at Shanghai Advanced Institute of Finance, Shanghai Jiaotong University. Previously, he held senior positions at various leading financial institutions for more than two decades in the areas of new product development, risk management, asset/liability management and investment analytics.
David has a PhD degree in statistics from the University of Waterloo, Master’s degrees in economics, finance and actuarial science, and a bachelor’s degree in mathematics. Dr. Li was one of the early practitioners in credit derivatives. His work of using copula functions for credit portfolio modeling has been widely cited by academic researchers, broadly used by practitioners for credit portfolio trading, credit risk management and credit rating, and well covered by media such as Wall Street Journal, Financial Times, Nikkei, CBC News.
Adjunct Professor, Department of Mathematics
PhD, University of Michigan, 2002
Non-Linear Option Pricing
Bryan Liang is an Adjunct Assistant Professor in the Department of Mathematics, specializing in Derivatives Modelling. Additionally, Liang has extensive experience as a quantitative analyst in the finance industry, currently working as a Quantitative Researcher in the Quantitative Financial Research Group for Bloomberg. Liang earned his Ph.D. in Mathematics from the University of Michigan.
Adjunct Professor, Department of Mathematics
PhD, Columbia University, 2011
Modeling and Trading Derivatives
Dr. Amal Moussa is a Managing Director at Goldman Sachs, where she leads the Single Stocks Exotic Derivatives Trading desk. Prior to that, Amal held senior-level positions in equity derivatives trading at other leading financial institutions such as J.P. Morgan, UBS, and Citigroup. In addition to her work in Markets, Amal is an Adjunct Professor at Columbia University, where she teaches a graduate course on Modeling and Trading Derivatives in the Mathematics of Finance Masters program.
Amal has a Ph.D. in Statistics, obtained with distinction, from Columbia University. Her thesis “Contagion and Systemic Risk in Financial Networks” shed light on the importance of the network structure in identifying systemic financial institutions and formulating regulatory policies and has been cited by several scholars and industry professionals, including former Federal Reserve president Janet Yellen. She was also awarded the Minghui Yu Teaching Award at Columbia University. Prior to her Ph.D., Amal graduated with a Masters in Mathematical Finance from Sorbonne University (former Paris VI) and a Grande Ecole engineering degree from Télécom Paris.
Amal is a board member of Teach for Lebanon, an NGO working to ensure that all children in Lebanon have access to education regardless of socioeconomic background, and she is an active member of the Women in Trading network at Goldman Sachs.
Adjunct Assistant Professor, Department of Mathematics
PhD, Columbia University, 1996
Programming for Quantitative & Computational Finance
Ka Yi Ng is an Adjunct Assistant Professor in the Department of Mathematics with extensive quantitative experience in FinTech. Currently, Ng works at Calypso Technology Inc. and serves as an advisor at Finch Lead Inc. Ng previously worked at Wall Street Systems and ION. At Columbia, her interests include Derivatives and Structured Products Development, and Machine Learning. Ng earned her Ph.D. in Mathematics from Columbia University.
Adjunct Professor, Department of Mathematics
PhD, University of Kentucky, 1983
Multi-Asset Portfolio Management
Colm O’Cinneide is an adjunct professor in the Department of Mathematics. He has worked in quantitative asset allocation and portfolio construction roles for the past 20 years at Deutsche Asset Management, QS Investors, and Franklin Templeton Investments, where he is currently an SVP. He was a partner at QS investors. Prior to this, he worked in academia from 1982 to 2000 and held tenured positions in Mathematical Sciences (Statistics) at the University of Arkansas and Industrial Engineering (Operations Research) at Purdue University. He has 40+ refereed publications related to probability, statistics, numerical analysis, and finance, with 1300+ citations and a track record of National Science Foundation funding. He has a PhD in Statistics from the University of Kentucky.
MBA, Finance, University of Chicago, 1999
Multi-Asset Portfolio Management
Editor-in-Chief of the Journal of Investment Consulting, Wealth Management eJournal, and Wealth Management Editor’s Choice eJournal; formerly Director of Investment Strategy at AB Bernstein; prior to that head of Strategic Asset Allocation Portfolio Management and partner at QS Investors, LLC and head of Strategic Asset Allocation Portfolio Management at Deutsche Asset Management; Past President and Director of the Honorary Board of the Society of Quantitative Analysts; MS in Mathematical Economics and ABD from Moscow State University; MBA from the University of Chicago (1999).
PhD, University of Brescia, 2000
Fixed Income Portfolio Management
Rosanna Pezzo-Brizio is an Adjunct Professor in the Department of Mathematics, specializing in Fixed Income Portfolio Management. Pezzo-Brizio has a vast array of professional, senior experience, working at Goldman Sachs, Greenwich Capital Markets, Intesa Sanpaolo. Currently, she is the Director of the Investment Consulting Group at New York Life Investments. Pezzo-Brizio holds a Ph.D. in Mathematics of Finance from the University of Brescia. Additionally, she graduated from Columbia University’s Mathematics of Finance program in 1998 as one of the program’s first classes.
Adjunct Assistant Professor, Department of Statistics
PhD, University of Oxford, 2016
Statistical Inference / Time-Series Modelling
fhr2111@columbia.edu
PhD, Harvard University
Machine Learning for Finance
Professor Ritter is founder and CIO of Ritter Alpha LP, a registered investment adviser running systematic absolute-return trading strategies across multiple asset classes and geographical regions. Before Ritter Alpha, he was a senior portfolio manager at GSA Capital and a Vice President in the Statistical Arbitrage Group at Highbridge Capital Management (HCM). Gordon completed his PhD in mathematical physics at Harvard University and his Bachelors’ degree with honors in Mathematics from the University of Chicago. While at Harvard, he published several papers in the areas of quantum field theory, differential geometry, quantum computation and abstract algebra. His current research is on portfolio optimization and statistical machine learning. Notable publications include “Optimal turnover, liquidity, and autocorrelation,” with @Bastien Baldacci of @ Université Paris Dauphine – PSL and @Jerome Benveniste of @New York University, Risk, 2022, and “Machine learning for trading,” Risk, 2017. In recognition of the latter publication, Professor Ritter was named Buy-Side Quant of the Year in 2019.
wgr2107@columbia.edu
Adjunct Assistant Professor, Department of Mathematics
MBA, Columbia Business School
Machine Learning for Finance
Renzo Silva is an Adjunct Assistant Professor in the Department of Mathematics. In addition to his teaching position, Mr. Silva has extensive professional experience in the Financial Technology industry, and he currently serves as a Software Engineering Manager at Google. Previous experiences include Software Development Manager at Amazon, CTO at P1 Capital, and Managing Director at the New York Stock Exchange. Mr. Silva is a graduate of Columbia University’s Mathematics of Finance MA program, and he also holds an MBA in Finance and Economics from Columbia Business School. His research interests include Artificial Intelligence and Machine Learning, Optimization, Simulation, and Quantum Computing.
Adjunct Associate Professor, Department of Mathematics
PhD, Sofia University
Stochastic Processes – Applications I
Iordan Slavov is AI/ML Technical Lead at JPMorgan Chase. Previously he has held analytical positions at Thomson Reuters, UnitedHealth Group and a few start-ups where he applied his expertise in Data Science, Machine Learning and Statistics. He has a PhD in Mathematics from Sofia University, Bulgaria and MA degrees in Statistics and Mathematics of Finance from Columbia University. He is also an Adjunct Associate Professor at CUNY where he teaches graduate classes in Statistics.
PhD, Princeton University, 1995
Introduction to the Mathematics of Finance
Mikhail Smirnov is a Senior Lecturer in Discipline in the Department of Mathematics and was Director of the Mathematics of Finance program in 1998-2012. His research interests include Quantitative Portfolio Management, Quantitative Investment Strategies, and Risk Measurement. He holds a Ph.D. from Princeton University.
smirnov@math.columbia.edu | 212-854-6955 | Website
PhD, University of California, Berkeley, 1991
Financial Risk Management and Regulation
Harvey Stein is a senior VP in the Labs group in Two Sigma where he works on various research projects around the firm. From 1993 to 2022, Dr. Stein was at Bloomberg, where he served as the head of several departments including Quantitative Risk Analytics, Counterparty and Credit Risk, Interest Rates Derivatives, and Quantitative Finance R&D. Harvey is well known in the industry, having published and lectured on credit risk modeling, financial regulation, interest rate and FX modeling, CVA calculations, mortgage backed security valuation, COVID-19 data analysis, and other subjects. Dr. Stein is on the board of directors of the IAQF, a board member of the Rutgers University Mathematical Finance program, an adjunct professor at Columbia University, and organizer of the IAQF/Thalesians financial seminar series. He’s also worked as a quant researcher on the Bloomberg for President campaign. Harvey holds a Ph.D. in Mathematics from the University of California, Berkeley (1991) and a B.S. in Mathematics from Worcester Polytechnic Institute (1982).
Statistical Interference/ Time-Series Modeling
Yisha Yao is an Assistant Professor with the Department of Statistics. Her research interests span a wide range of modern high-dimensional statistics, including but not limited to nonparametric methods, statistical inferences, mixture models, FDR control, iterative algorithms, tensor analysis, and applications in biomedical sciences. She obtained her PhD in statistics from Rutgers University (New Brunswick) in 2021, and then spent two years at Yale University as a postdoctoral researcher in biostatistics.
Adjunct Professor, Department of Mathematics
AB/SM, Harvard University, 1998
Hedge Funds Strategies and Risk
Eric Yeh is an Adjunct Professor in the Department of Mathematics, specializing in Quantitative Investment Strategies. Yeh’s vast professional experience in the Finance industry includes senior positions at Morgan Stanley, Deutsche Bank, Tower Research Capital, and AllianceBernstein. Currently, he is President of Vermillion Leaf Capital LLC and an advisor to multiple investment managers, including the $100M hedge fund he previously co-founded. Yeh holds an AB in Mathematics and an SM in Computer Science from Harvard University.