For undergraduates only. Examines the fundamental concepts of financial accounting and finance, from the perspective of both managers and investors. Key topics covered include principles of accrual accounting; recognizing and recording accounting transactions; preparation and analysis of financial statements; ratio analysis; pro-forma projections; time value of money (present values, future values and interest/discount rates); inflation; discounted-cash-flow (DCF) project evaluation methods; deterministic and probabilistic measures of risk; capital budgeting.
Designed to provide an introduction to data science for sophomore SEAS majors. Combines three perspectives: inferential thinking, computational thinking, and real-world applications. Given data arising from some real-world phenomenon, how does one analyze that data so as to understand that phenomenon? Teaches critical concepts and skills in computer programming, statistical inference, and machine learning, in conjunction with hands-on analysis of real-world datasets such as economic data, document collections, geographical data, and social networks. At least one project will address a problem relevant to New York City.
Some of the main stochastic models used in engineering and operations research applications: discrete-time Markov chains, Poisson processes, birth and death processes and other continuous Markov chains, renewal reward processes. Applications: queueing, reliability, inventory, and finance. IEOR E3106 must be completed by the fifth term. Only students with special academic circumstances may be allowed to take these courses in alternative semesters with the consultation of CSA and Departmental advisers.
This first course in optimization focuses on theory and applications of linear optimization, network optimization, and dynamic programming.
Introductory course to probability theory and does not assume any prior knowledge of subject. Teaches foundations required to use probability in applications, but course itself is theoretical in nature. Basic definitions and axioms of probability and notions of independence and conditional probability introduced. Focus on random variables, both continuous and discrete, and covers topics of expectation, variance, conditional distributions, conditional expectation and variance, and moment generating functions. Also Central Limit Theorem for sums of random variables. Consists of lectures, recitations, weekly homework, and in-class exams.
Independent work involving experiments, computer programming, analytical investigation, or engineering design.
Independent work involving experiments, computer programming, analytical investigation, or engineering design.
Introduction to the economic evaluation of industrial projects. Economic equivalence and criteria. Deterministic approaches to economic analysis. Multiple projects and constraints. Analysis and choice under risk and uncertainty.
A graduate course only for MS&E, IE, and OR students. This is also required for students in the Undergraduate Advanced Track. For students who have not studied linear programming. Some of the main methods used in IEOR applications involving deterministic models: linear programming, the simplex method, nonlinear, integer and dynamic programming.
Linear, quadratic, nonlinear, dynamic, and stochastic programming. Some discrete optimization techniques will also be introduced. The theory underlying the various optimization methods is covered. The emphasis is on modeling and the choice of appropriate optimization methods. Applications from financial engineering are discussed.
Probability and simulation. Statistics building on knowledge in probability and simulation. Point and interval estimation, hypothesis testing, and regression. A specialized version of IEOR E4150 for MSE and MSBA students who are exempt from the first half of IEOR E4101. Must obtain waiver for E4101.
Basic probability theory, including independence and conditioning, discrete and continuous random variable, law of large numbers, central limit theorem, and stochastic simulation, basic statistics, including point and interval estimation, hypothesis testing, and regression; examples from business applications such as inventory management, medical treatments, and finance. A specialized version of IEOR E4150 for MSE and MSBA students.
Some of the main stochastic models used in engineering and operations research applications: discrete-time Markov chains, Poisson processes, birth and death processes and other continuous Markov chains, renewal reward processes. Applications: queueing, reliability, inventory, and finance.
Aims to develop and harness the modeling, analytical, and managerial skills of engineering students and apply them to improve the operations of both service and manufacturing firms. Structured as a hands-on laboratory in which students "learn by doing" on real-world consulting projects (October to May). The student teams focus on identifying, modeling, and testing (and sometimes implementing) operational improvements and innovations with high potential to enhance the profitability and/or achieve sustainable competitive advantage for their sponsor companies. The course is targeted toward students planning careers in technical consulting (including operations consulting) and management consulting, or pursuing positions as business analysts in operations, logistics, supply chain and revenue management functions, positions in general management, and future entrepreneurs.
Covers the following topics: fundamentals of probability theory and statistical inference used in engineering and applied science; Probabilistic models, random variables, useful distributions, expectations, law of large numbers, central limit theorem; Statistical inference: pint and confidence interval estimation, hypothesis tests, linear regression. For IEOR graduate students.
Zero-credit course. Primer on quantitative and mathematical concepts. Required for all incoming MSOR and MSIE students.
Open to SEAS graduate and advanced undergraduate students, Business School, and GSAPP. Students from other schools may apply. Fast-paced introduction to human-centered design. Students learn the vocabulary of design methods, understanding of design process. Small group projects to create prototypes. Design of simple product, more complex systems of products and services, and design of business.
Required for undergraduate students majoring in IE. Sensory and cognitive (brain) processing considerations in the design, development, and operations of systems, products, and tools. User or operator limits and potential in sensing, perceiving decision making, movement coordination, memory, and motivation.
Surveys tools available in Python for getting (web scraping and APIs) and visualizing data (charts and maps). Introduction to analytics through machine learning (ML algorithms, model evaluation, text analytics, network algorithms, deep learning).
Descriptive statistics, central limit theorem, parameter estimation, sufficient statistics, hypothesis testing, regression, logistic regression, goodness-of-fit tests, applications to operations research models.
Zero-credit course. Primer on quantitative and mathematical concepts. Required for all incoming MSOR and MSIE students.
Interpret financial statements, build cash flow models, value projects, value companies, and make Corporate Finance decisions. Additional topics include: cost of capital, dividend policy, debt policy, impact of taxes, Shareholder/Debtholder agency costs, dual-class shares, using option pricing theory to analyze management behavior, investment banking activities, including equity underwriting, syndicated lending, venture capital, private equity investing and private equity secondaries. Application of theory in real-world situations: analyzing financial activities of companies such as General Electric, Google, Snapchat, Spotify, and Tesla.
Required for students in the Undergraduate Advanced Track. Key measures and analytical tools to assess the financial performance of a firm and perform the economic evaluation of industrial projects. Deterministic mathematical programming models for capital budgeting. Concepts in utility theory, game theory and real options analysis.
Generation of random numbers from given distributions; variance reduction; statistical output analysis; introduction to simulation languages; application to financial, telecommunications, computer, and production systems. Graduate students must register for 3 points. Undergraduate students must register for 4 points. Note: Students who have taken IEOR E4703 Monte Carlo simulation may not register for this course for credit. Recitation section required.
Required for undergraduate students majoring in OR:FE and OR. A mathematically rigorous study of game theory and auctions, and their application to operations management. Topics include introductory game theory, private value auction, revenue equivalence, mechanism design, optimal auction, multiple-unit auctions, combinatorial auctions, incentives, and supply chain coordination with contracts. No previous knowledge of game theory is required.
We will take a hands-on approach to developing computer applications for Financial Engineering. Special focus will be placed on high-performance numerical applications that interact with a graphical interface. In the course of developing such applications we will learn how to create DLLs, how to integrate VBA with C/C++ programs, and how to write multithreaded programs. Examples of problems settings that we consider include simulation of stock price evolution, tracking, evaluation and optimization of a stock portfolio; optimal trade execution. In the course of developing these applications, we review topics of interest to OR:FE in a holistic fashion.
MS IEOR students only. Introduction programming in Python, tools with the programmer's ecosystem. Python, Data Analysis tools in Python (NumPy, pandas, bokeh), GIT, Bash, SQL, VIM, Linux/Debia, SSH.
Zero-credit course. Primer on Python for analytics concepts. Required for MSBA students.
IEOR students only. Understand digital businesses, apply scientific, engineering thinking to digital economy. Data-driven digital strategies and operating models. Sectors: ecommerce, advertising technology, and marketing technology. Automation of the marketing, sales, and advertising functions. Algorithms, patents, and business models. Business side of the digital ecosytem and the digital economy.
Teams of students work on real-world projects in analytics. Focus on three aspects of analytics: identifying client analytical requirements; assembling, cleaning and organizing data; identifying and implementing analytical techniques (e.g., statistics and/or machine learning); and delivering results in a client-friendly format. Each project has a defined goal and pre-identified data to analyze in one semester. Client facing class. Class requires 10 hours of time per week and possible client visits on Fridays.
IEOR students only; priority to MSBA students. Survey tools available in Python for getting, cleaning, and analyzing data. Obtain data from files (csv, html, json, xml) and databases (Mysql, PostgreSQL, NoSQL), cover the rudiments of data cleaning, and examine data analysis, machine learning, and data visualization packages (NumPy, pandas, Scikit-lern, bokeh) available in Python. Brief overview of natural language processing, network analysis, and big data tools available in Python. Contains a group project component that will require students to gather, store, and analyze a data set of their choosing.
MS IEOR students only. Introduction to machine learning, practical use of ML algorithms and applications to financial engineering and operations. Supervised learning: regression, classification, resampling methods, regularization, support vector machines (SVMs), and deep learning. Unsupervised learning: dimensionality reduction, matrix decomposition, and clustering algorithms.
To introduce students to programming issues around working with clouds for data analytics. Class will learn how to work with infrastructure of cloud platforms, and discussion about distributed computing, focus of course is on programming. Topics covered include MapReduce, parallelism, rewriting of algorithms (statistical, OR, and machine learning) for the cloud, and basics of porting applications so that they run on the cloud.
Markov Decision Processes (MDP) and Reinforcement Learning (RL) problems. Reinforcement Learning algorithms including Q-learning, policy gradient methods, actor-critic method. Reinforcement learning while doing exploration-exploitation dilemma, multi-armed bandit problem. Monte Carlo Tree Search methods, Distributional, Multi-agent, and Causal Reinforcement Learning.
This course will cover the basics of game theory and market design, with a focus on how AI and optimization enables large-scale game solving and markets. We will cover the core ideas behind recent superhuman AIs for games such as Poker. Then, we will discuss how AI and game theory ideas are used in marketplaces such as internet advertising, fair course seat allocation, and spectrum reallocation. This is intended to be an advanced MS level and senior undergraduate course for students in Operations Research and Financial Engineering.
Data visualization and how to build a story with data. Using complex data or statistics to communicate results effectively. Learn to present analysis and results conscisely and effectively.
OKR framework and different variations. Measurement techniques (A/B testing, validation, correlation, etc.) Identifying what to measure in product experience and business initiatives. Data-driven decision making.
Applied Analytics focus querying and transforming data with SQL, defining and visualizing metrics, measuring impact of products / processes. Tools and techniques to convert raw data to business decisions, statistical analysis. Be able to apply these techniques to real-world datasets.
Course covers major statistical learning methods for data mining under both supervised and unsupervised settings. Topics covered include linear regression and classification, model selection and regularization, tree-based methods, support vector machines, and unsupervised learning. Students learn about principles underlying each method, how to determine which methods are most suited to applied settings, concepts behind model fitting and parameter tuning, and how to apply methods in practice and assess their performance. Emphasizes roles of statistical modeling and optimization in data mining.
This course is designed as an introductory exposure to entrepreneurial concepts and practical skills for engineering students (and others) who wish to explore entrepreneurship conceptually or as a future endeavor in their careers. The class will be a mix of lecture, discussion, team-building and in-the-field workshopping of concepts we cover.
The last decade of 20 th century witnessed a rapid convergence of three C’s: Communications, Computers, and Consumer Electronics. This convergence has given us the Internet, smart phones, and an abundance of data with Data Science playing a major role in analyzing these data and providing predictive analytics that lead to actionable items in many fields and businesses. Finance is a field with a large amount of information and data that can utilize the skills of Data Scientists, however, to be effective in this field a data scientist, in addition to analytic knowledge, should also be knowledgeable of the working, instruments, and conventions of financial markets that range from Foreign Exchange to Equities, Bonds, Commodities, Cryptocurrencies and host of other asset classes. The objective of this course is to provide Data Science students with a working knowledge of major areas of finance that could help them in finding a position in the Financial Industry. The wide range of topics covered in this course besides expanding the range of positions where students could be a fit, it gives them more flexibility in their job search. The course will also be of value to them in managing their own finances in the future.
Each offering of this course is devoted to a particular sector of Operations Research and its contemporary research, practice, and approaches. If topics are different, then course can be taken more than once for credit.
This Columbia University course offers a project-based learning experience focused on systematic quantitative investment. It covers the full data science workflow, from concept to performance evaluation. Students will engage in a real-time financial forecasting competition, using open-source financial and alternative data, to make and present investment decisions. Ideally, this course suits students aspiring to careers as quants or data scientists in the financial sector.
The course focuses on a PRACTICAL study of how to quantify & predict RISK in organizations by using learnings from: Regression analysis; Monte Carlo simulation; Factor analysis; Cohort analysis; Cluster analysis; Time series analysis; Sentiment analysis. Expectation is that incoming students should have a basic understanding of such concepts and statistics. The course will offer meeting & listening to CXO's & top executives from companies who have implemented robust AI & Applied Risk solutions to solve real-world problems in their own industries.
It will give students a great opportunity to learn practical applications of predictive analytics to solve real business problems
A project-based course in Forecasting, predicting a time series into the future, to prepare students for real-world applications including articulating the business case, value creation, problem statement, and the iterative development of solutions including building a data pipeline, exploration, modeling, and visualizations. The course will use Statistical methods, Machine Learning, and Deep Learning with Transformer-based methods to predict a time series. It will use nuggets of signal processing to augment Machine Learning models to characterize and filter orders of dynamics in the time series data.
In this course, you'll leverage student engagement data to create a photo and text recommendation app similar to Instagram/Twitter. This app will utilize AI-generated photos and text and require you to recommend a feed from over 500,000 pieces of AI generated content. We'll explore various techniques to achieve this, including, but not limited to: Candidate Generation (Collaborative filtering, Trending, Cold start, N-tower neural network models, Cross-attention teachers, Distillation, Transfer learning, Random graph walking, Reverse indexes, LLMs as embedding), Filtering (Small online models, Caching, Deduplication, Policy), Prediction/Bidding (User logged activity based prediction (time-series), Multi-gate mixture of experts (MMOE), Regularization, Offline/Online evaluation (NDCG, p@k, r@k), Boosted Trees, Value Based Bidding), Ranking (Re-ranking, Ordering, Diversity, Enrich/Metadata/Personalization, Value Functions), Misc (Data Privacy and AI Ethics, Creator Based Models, Declared, Explicit and implicit topics, Explore/Exploit, Interpret/Understand/Context/Intention).
These concepts are applicable to various recommendation systems, from e-commerce to travel to social media to financial modeling. The instructor's experience at Uber Eats, Facebook, Instagram, and Google will provide valuable insights into real-world use cases.
Primer on quantitative and mathematical concepts. Required for all incoming MSBA students.
Risk management models and tools; measure risk using statistical and stochastic methods, hedging and diversification. Examples include insurance risk, financial risk, and operational risk. Topics covered include VaR, estimating rare events, extreme value analysis, time series estimation of extremal events; axioms of risk measures, hedging using financial options, credit risk modeling, and various insurance risk models.
Required for undergraduate students majoring in OR:FE. Characteristics of commodities or credit derivatives. Case study and pricing of structures and products. Topics covered include swaps, credit derivatives, single tranche CDO, hedging, convertible arbitrage, FX, leverage leases, debt markets, and commodities.
Prepares students to gather, describe, and analyze data, using advanced statistical tools to support operations, risk management, and response to disruptions. Analysis is done by targeting economic and financial decisions in complex systems that involve multiple partners. Topics include probability, statistics, hypothesis testing, experimentation, and forecasting.
Prerequisite(s): IEOR E4106 or E3106. Required for undergraduate students majoring in OR:FE. Introduction to investment and financial instruments via portfolio theory and derivative securities, using basic operations research/engineering methodology. Portfolio theory, arbitrage; Markowitz model, market equilibrium, and the capital asset pricing model. General models for asset price fluctuations in discrete and continuous time. Elementary introduction to Brownian motion and geometric Brownian motion. Option theory; Black-Scholes equation and call option formula. Computational methods such as Monte Carlo simulation.
This graduate course is only for M.S. Program in Financial Engineering students, offered during the summer session. Review of elements of probability theory, Poisson processes, exponential distribution, renewal theory, Wald’s equation. Introduction to discrete-time Markov chains and applications to queueing theory, inventory models, branching processes.
This graduate course is only for M.S. Program in Financial Engineering students, offered during the summer session. Discrete-time models of equity, bond, credit, and foreign-exchange markets. Introduction to derivative markets. Pricing and hedging of derivative securities. Complete and incomplete markets. Introduction to portfolio optimization and the capital asset pricing model.
An introduction to capital markets and investments providing an overview of financial markets and tools for asset valuation. Topics covered include the pricing of fixed-income securities (treasury markets, interest rate swaps futures, etc.), discussions on topics in credit, foreign exchange, sovereign ad securitized markets—private equity and hedge funds, etc.
Stochastic control has broad applications in almost every walk of life, including finance, revenue management, energy, health care and robotics. Classical, model-based stochastic control theory assumes that the system dynamics and reward functions are known and given, whereas modern, model-free stochastic control problems call for reinforcement learning to learn optimal policies in an unknown environment. This course covers model-based stochastic control and model-free reinforcement learning, both in continuous time with continuous state space and possibly continuous control (action) space. It includes the following topics: Shortest path problem, calculus of variations and optimal control; formulation of stochastic control; maximum principle and backward stochastic differential equations; dynamic programming and Hamilton-Jacobi-Bellman (HJB) equation; linear-quadratic control and Riccati equations; applications in high-frequency trading; exploration versus exploitation in reinforcement learning; policy evaluation and martingale characterization; policy gradient; q-learning; applications in diffusion models for generative AI.
ESG (Environmental, Social and Corporate Governance) Finance is a rapidly growing area of Investment Management – and Finance more broadly – that has received a lot of attention in the past several years from the investor community, financial regulatory agencies, and the general public alike. This course provides an introduction to ESG Finance from a financial engineer’s perspective. This course also discusses proliferation of newly available data sources and the associated quantitative techniques necessary to process those. A major component of this course is a discussion of Climate Risk, an area of particular focus due to its increasing general importance. The course includes an overview of both recent research and the evolving regulatory landscape in the climate risk space. An in-depth discussion of financial impact assessment of various climate risk-driven scenarios (climate risk stress testing) concludes the course.
In this course, we will cover the basics of mathematical modeling of interest rates and credit derivatives. In the first part, we will cover basic interest rate derivatives, the Heath-Jarrow-Morton (HJM)
framework, classic short rate models (for both interest rates and default intensities), and the numerical techniques used in practice for their calibration. In the second part, we will cover the basics
of single-name derivatives modeling, and we will discuss pricing simple credit derivatives. We will also discuss correlation products and the most common techniques used for their pricing. In the third part, we will discuss some recent research papers addressing the use of adjoint algorithmic differentiation for the calculation of risk for interest rate and credit derivatives.
The search for better performance has led investors to explore Alternative Investments that are outside the traditional categories of exchange traded equities, Treasury Bonds, and other
investment-grade fixed income products. The field of Alternative Investments covers a wide range of products such as convertible bonds, Preferred Shares, Hedge Funds, Venture Capital, and
Cryptocurrencies. There is a growing need in the market for students with knowledge of these products and the practical and theoretical know how of valuing and risk managing these investments given that each product has it own nuances and anomalies. This course presents and studies some major Alternative Investment products and ways to evaluate and risk manage them.
Introduction to quantitative modeling of credit risk, with a focus on the pricing of credit derivatives. Focus on the pricing of single-name credit derivatives (credit default swaps) and collateralized debt obligations (CDOs). Detail topics include default and credit risk, multiname default barrier models and multiname reduced form models.
Foreign exchange market and its related derivative instruments—the latter being forward contracts, futures, options, and exotic options. What is unusual about foreign exchange is that although it can rightfully claim to be the largest of all financial markets, it remains an area where very few have any meaningful experience. Virtually everyone has traded stocks, bonds, and mutual funds. Comparatively few individuals have ever traded foreign exchange. In part that is because foreign exchange is an interbank market. Ironically the foreign exchange markets may be the best place to trade derivatives and to invent new derivatives—given the massive two-way flow of trading that goes through bank dealing rooms virtually 24 hours a day. And most of that is transacted at razor-thin margins, at least comparatively speaking, a fact that makes the foreign exchange market an ideal platform for derivatives. The emphasis is on familiarizing the student with the nature of the foreign exchange market and those factors that make it special among financial markets, enabling the student to gain a deeper understanding of the related market for derivatives on foreign exchange.
Prerequisite(s): IEOR E4700. Conceptual and practical understanding of structured and hybrid products from the standpoint of relevant risk factors, design goals and characteristics, pricing, hedging, and risk management. Detailed analysis of the underlying cash-flows, embedded derivative instruments, and various structural features of these transactions, both from the investor and issuer perspectives, and analysis of the impact of the prevailing market conditions and parameters on their pricing and risk characteristics. Numerical methods for valuing and managing risk of structured/hybrid products and their embedded derivatives and their application to equity, interest rates, commodities and currencies, inflation, and credit-related products. Conceptual and mathematical principles underlying these techniques, and practical issues that arise in their implementations in the Microsoft Excel/VBA and other programming environments. Special contractual provisions encountered in structured and hybrid transactions, and incorporation of yield curves, volatility smile, and other features of the underlying processes into pricing and implementation framework for these products.