TEACHING

Courses:

Stony Brook University (2020- ):

1 x Data Mining (undergraduate)
3 x Financial Derivatives & Stochastic Calculus (graduate + Ph.D.)
1 x Quantitative Risk Management (graduate)
3 x Machine Learning in Quantitative Finance (graduate + Ph.D.)

Stevens Institute of Technology (2019-2020):

1 x Time Series (graduate + Ph.D.)
2 x Linear Algebra (undergraduate)
1 x Statistical Learning with R & Python (graduate)

Columbia University (2015-2019):

3 x Statistical Methods for Finance (graduate)
2 x Time Series Modeling and Statistical Inference (graduate)
2 x Stochastic Methods in Finance (graduate)
1 x Modern Multivariate Statistical Inference (graduate)
2 x Nonparametric Statistics (graduate)
1 x Data Mining (graduate)
2 x Linear Regression Models (graduate)

Recommended textbooks for my courses

Details of each course

Financial Derivatives & Stochastic Calculus

1 x Spring 2021 (Stony Brook University, Graduate Course)

Textbooks:Steven Shreve, Stochastic Calculus for Finance I --The Binomial Asset Pricing ModelSteven Shreve, Stochastic Calculus for Finance II -- Continuous-Time ModelsTomas Bjork Arbitrage Theory in Continuous TimeMathematical theory and probabilistic tools for modeling and analyzing security markets are developed. Topics include: derivative security, no-arbitrage pricing, binomial model, risk-neutral pricing, utility maximization, optimal stopping problem, American option, trinomial model, incomplete markets, Brownian motion, reflection principle, barrier option, Stochastic integral, Ito's formula, Risk-neutral measure, Black-Scholes model, market completeness, Fundamental Theorem of Asset Pricing, Greeks, implied volatility, American option, variational inequality, free-boundary problem, change of numeraire, exchange rate, currency derivative, term structure of interest rates.

Quantitative Risk Management

1 x Spring 2021 (Stony Brook University, Graduate Course)

Textbook:Quantitative Risk Management: Concepts, Techniques and Tools - Revised Edition Alexander J. McNeil, Rüdiger Frey, and Paul EmbrechtsThis selective course in quantitative finance covers intensively various topics in quantitative risk management and related statistical tools: Basic Concepts in Risk Management, Multivariate Models, Financial Time Series, Copulas and Dependence, Aggregate Risk, Extreme Value Theory, Credit Risk Management, Dynamic Credit Risk Models, and Operational Risk and Insurance Analytics.

Machine Learning in Quantitative finance

1 x Fall 2021 (Stony Brook University, Graduate + PhD Course)

Textbook: Machine Learning in Finance: From Theory to Practice 1st ed. 2020 Edition, by Matthew F. Dixon, Igor Halperin, and Paul Bilokon
Topics in probabilistic modeling: Bayesian vs. frequentist estimation, bias-variance tradeoff, sequential Bayesian updates, model selection and model averaging; Probabilistic graphical models and mixture models; Multiplicative Weights Update Method; Bayesian regression and Gaussian processes.Topics in feedforward neural networks: Feedforward architecture; Stochastic gradient descent and backpropagation algorithm; Non-Linear Factor Modeling and applications in asset pricing; Convolutional neural networks; Autoencoders.Methods for sequential learning: Linear time series models; Probabilistic sequence modeling – Hidden Markov Models and particle filtering; Recurrent Neural Networks; Applications in finance.Dynamic programming and reinforcement learning algorithms: Markov decision process and dynamic programming methods (Bellman equations and Bellman optimality); Reinforcement learning methods (Monte-Carlo methods, policy-based learning, TD-learning, SARSA and Q-learning); Deep reinforcement learning; Applications of reinforcement learning in finance.

Time series

1xSpring 2020 (Stevens Institute of Technology, Graduate + PhD Course)

Textbooks:Robert H. Shumway , David S. Stoffer, Time Series Analysis and Its Applications: With R Examples 4th ed. 2017 EditionCourse introduces time series models and their applications to modeling and prediction. It utilizes real-world examples to apply variety of time series models and methods. After successful completion of this course, students will have a good understanding of the following topics and their applications: stationarity and measures of dependency; time series regression, graphical analysis, trend and seasonality detection and removal, and moving-average filtering; linear time series analysis and its applications; spectral analysis: periodogram testing for seasonality and periodicities, the maximum entropy and maximum-likelihood estimators; additional topics: long-memory processes, unit root testing, and volatility modeling; state space models and Kalman filtering.

Linear Algebra

2 x Fall 2019, Spring 2020 (Stevens Institute of Technology, Undergraduate Course)

Textbooks: Gilbert Strang, Introduction to Linear Algebra, Fifth Edition (2016)Gilbert Strang, Linear Algebra and Learning from Data, (2019)The objective of this course is to introduce the students to linear algebra and demonstrate some of its applications. This course builds a foundation for many other courses in mathematics, as well as computational engineering, statistics, machine learning, and quantitative methods in finance and management. After successful completion of this course, students will have a good understanding of the following topics and their applications: Systems of linear equations, Row reduction and echelon forms, Matrix operations, including inverses, Block matrices, Linear dependence and independence, Subspaces and bases and dimensions, Orthogonal bases and orthogonal projections, Gram-Schmidt process, Linear models and least-squares problems, Determinants and their properties, Cramer's Rule, Eigenvalues and eigenvectors, Diagonalization of a matrix, Symmetric matrices, Positive definite matrices, Similar matrices, Linear transformations, Singular Value Decomposition.

Statistical Learning with r & python

1 x Fall 2019 (Stevens Institute of Technology, Graduate Course)

Textbook: Gareth James, Daniela Witten, Trevor Hastie and Robert Tibshirani , An Introduction to Statistical LearningThe objective of this course is to introduce the students to a broad spectrum of methods in the field of statistical learning. We will start by reviewing the fundamentals on statistical estimation and inference. Then we will cover linear regression, Ridge regression, LASSO, elastic-net, maximum likelihood estimation, maximum a posterior estimation, cross-validation and bootstrap, expectation-maximization algorithm, ANOVA, and classification. Then we will move to generalized linear models which encompasses linear and logistic regression. Next we will cover generalized additive models, basis expansion, and smoothing. Finally, we will introduce random forest and regression trees, support vector machines, and principal component analysis.

Statistical Methods for Finance

3 x Summer 2017, Summer 2018, and Summer 2019, (Columbia University, Graduate Course)

Textbook: T.L. Lai and H. Xing, Statistical Models and Methods for Financial MarketsThe course provides a broad and systematic introduction to statistical methods applied in finance. It covers simple and multiple linear regression, multivariate analysis, and maximum likelihood estimation. These statistical methods are applied in Markowitz's portfolio theory, CAPM, and multifactor pricing models. Next the course covers univariate and multivariate linear time series models. Including ARMA, vector autoregressive models, and unit-root nonstationary ARIMA models. Next, it covers some of the main volatility models of asset returns such as univariate and multivariate GARCH models, and volatility estimators based on OHLC prices. Second part of the course focuses on selected advanced statistical topics and their applications in quantitative finance. Including, canonical correlation analysis, multivariate linear regression, penalized linear regression, Cholesky decomposition, PCA, and Cointegrated VAR models. During the course we will learn how to apply aforementioned techniques (i) to improve portfolio performance, (ii) quantify risk of the portfolio using risk measures such as Value-at-Risk and Expected Shortfall, and (iii) to develop statistical trading strategies such as pairs trading. Last lectures discuss high-frequency data, market microstructure, and associated trading strategies. Examples are given in R and Python.

Time Series Modeling and Statistical Inference

2 x Fall 2016, and Fall 2018, (Columbia University, Graduate Course)

Textbooks: Time Series Analysis and its Applications, Robert H. Shumway and David S. Stoffer (2017), 4th editionIntroduction to Time Series and Forecasting by Peter J. Brockwell and Richard A. DavisTime Series: Theory and Methods by Peter J. Brockwell and Richard A. DavisAnalysis of Financial Time Series, Ruey S. Tsay, 3rd EditionThe course provides a broad and systematic introduction to time series models and their applications to modeling and prediction of financial data. It utilizes real-world examples and real financial data to apply variety of time series models and methods. We will cover parameter estimation, filtering and predictions from ARMA, ARCH, GARCH and other nonlinear models; high-frequency data analysis; multivariate time series analysis; multivariate volatility modeling; portfolio optimization and risk prediction. The course will include additional coverage of modern day topics such as statistical arbitrage, pairs trading, and realized volatility; examples will be given in R.In particular, we cover: Financial time series and their characteristics, Linear time series analysis, causal processes, stationarity, and invertibility for AR, MA, ARMA, ARIMA, and SARIMA models and their applications, Deterministic trend vs. stochastic trend and unit-root processes, Conditional heteroscedastic models (ARCH and GARCH), High-frequency data analysis and its applications, Multivariate time series analysis and its applications (VAR, VMA, and VARMA models), Cointegration analysis, error correction model and its application in pairs trading, Principal component analysis and factor (Fama-French, BARRA, latent) models, Multivariate volatility models and their applications (MGARCH, CCC, DCC, and Cholesky), Applications for value at risk prediction and portfolio optimization.

Stochastic Methods in Finance

2 x Spring 2018 and Spring 2019, (Columbia University, Graduate Course)

Modern Multivariate Statistical Inference

1 x Spring 2017, (Columbia University, Graduate Course)

Textbook: Alan J. Izenman, Modern Multivariate Statistical Techniques: Regression, Classification, and Manifold LearningThe goal is to learn key elements of multivariate statistical inference. We will cover classical multivariate techniques and new algorithmic techniques for analyzing large multivariate data sets. The course will present the current state of multivariate statistical analysis in an age of high speed computation and large data sets. The material of this course has a broad application to scientific research (biology, chemistry, medicine, psychology, etc.) and also insurance and finance professionals (actuaries, quants). Completing this course should provide a fundamental basis for modern statistical data exploration.After an introductory segment on matrix algebra we discover topics such as multivariate normal distribution, multiple regression, regularized regression (LASSO, Ridge, Garotte and elastic Net), multivariate regression, principal components, canonical variate and correlation analysis, discriminant analysis, cluster analysis, and factor analysis, multivariate mixture of normal distribution and Expectation Maximization algorithm, support vector machine, and support vector regression.

Nonparametric Statistics

2 x Fall 2016, and Spring 2017, (Columbia University, Graduate Course)

Textbooks: J. J. Higgins, Introduction to modern nonparametric statisticsT. Hastie, R. Tibshirani, J. Friedman, The Elements of Statistical LearningL. Wasserman, All of nonparametric statisticsB. Efron, R. Tibshirani, Introduction to BootstrapE. Lehman, Nonparametrics: statistical methods based on ranks J. Gibbons, S. Chakraborti, Nonparametric statistical inferenceA. Tsybakov, Introduction to nonparametric estimationThis course provides an introduction to nonparametric estimation and testing:Topics on estimation include: curve fitting, locally linear polynomial, bias/variance trade-off, splines, cross validation. parameteric bootstrap, nonparametric bootstrap.Topics on testing include: goodness of fit tests including chi-square test, Kolmogorov-Smirnov test, Cramer-von Mises test, Anderson and Darling test, one and two sample nonparametric tests including sign test, rank test, Wilcoxon's test, Kruskal-Wallis test, and Friedman test. Measures of association such as Spearman's rank correlation and Kendall's Tau.

Data Mining

1 x Summer 2016, (Columbia University, Graduate Course)

Textbook: Kevin P. Murphy, Machine Learning A Probabilistic PerspectiveThe course covers basic concepts and the powerful modern methods from machine learning and data mining. In particular, it covers: Generative models for discrete data, Gaussian models, Bayesian statistics vs. frequentist statistics, Linear regression, Logistic regression, Generalized linear models and the exponential family, Mixture models and the EM algorithm, Latent linear models (including Factor Analysis, PCA, and ICA), Sparse linear models (including l_1 regularization methods and their extensions), Kernels (including kernel PCA, and Support Vector Machines), Gaussian processes, Adaptive basis function models (including classification and regression trees and boosting), Clustering (including spectral clustering and hierarchical clustering).

Linear Regression Models

2 x Fall 2015, and Spring 2016, (Columbia University, Graduate Course)

Textbooks:Michael Kutner, Christopher Nachtsheim, and John Neter, Applied Linear Regression ModelsTrevor Hastie, Robert Tibshirani, and Jerome Friedman,The Elements of Statistical Learning: Data Mining, Inference, and PredictionIn this class we study theory and practice of regression analysis, simple and multiple regression, including testing, estimation, and confidence procedures, modeling, regression diagnostics and plots, polynomial regression, colinearity and confounding, model selection, geometry of least squares. We cover also shrinkage and selection methods for linear regression (LARS, LASSO, Ridge regression, and Elastic-Net). This course requires extensive use of the computer to analyse data.

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