Operations Research and Financial Engineering

A first introduction to probability and statistics. This course will provide background to understand and produce rigorous statistical analysis including estimation, confidence intervals, hypothesis testing and regression and classification. Applicability and limitations of these methods will be illustrated using a variety of modern real world data sets and manipulation of the statistical software R. Prerequisite: MAT 201 concurrently or equivalent. Two lectures, one precept.

This course focuses on analytical and computational tools for optimization. We will introduce least-squares optimization with multiple objectives and constraints. We will also discuss linear optimization modeling, duality, the simplex method, degeneracy, interior point methods and network flow optimization. Finally, we will cover integer programming and branch-and-bound algorithms. A broad spectrum of real-world applications in engineering, finance and statistics is presented. Prerequisite MAT 202 or 204. Two lectures, one precept.

An introduction to probability and its applications. Topics include: basic principles of probability; Lifetimes and reliability, Poisson processes; random walks; Brownian motion; branching processes; Markov chains. Prerequisite: MAT 201, 203, or 216. Three lectures, one precept.

A survey of quantitative approaches for making optimal decisions under uncertainty, including decision trees, Monte Carlo simulation, and stochastic programs. Forecasting and planning systems are integrated in the context of financial applications. Machine learning methods are linked to the stochastic optimization models. Prerequisites: ORF 307 or MAT 305, and ORF 309. Two 90-minute classes, one precept.

Financial Mathematics is concerned with designing and analyzing products that improve the efficiency of markets, and create mechanisms for reducing risk. This course develops quantitative methods for these goals: the notions of arbitrage and risk-neutral pricing in discrete time, specific models such as Black-Scholes and Heston in continuous time, and calibration to market data. Credit derivatives, the term structure of interest rates, and robust techniques in the context of volatility options will be discussed, as well as lessons from the financial crisis. Prerequisites: ORF 309, ECO 100, and MAT 104. Two lectures, one precept.

This course is a theoretically oriented introduction to the statistical tools that underpin modern machine learning, whose hallmarks are large datasets and/or complex models. Topics include a rigorous analysis of dimensionality reduction, a survey of models ranging from regression to neural networks, and an analysis of learning algorithms.. Prerequisites: Probability at the level of ORF 309. Statistics at the level of ORF 245. Linear Algebra at the level of MAT 202 or permission of instructor. Two lectures, one precept.

An introduction to several fundamental and practically-relevant areas of modern optimization and numerical computing. Topics include computational linear algebra, first and second order descent methods, convex sets and functions, basics of linear and semidefinite programming, optimization for statistical regression and classification, and techniques for dealing with uncertainty and intractability in optimization problems. Extensive hands-on experience with high-level optimization software. Applications drawn from operations research, statistics and machine learning, economics, control theory, and engineering.

A course covering special topics in operations research or financial engineering. Subjects may vary from year to year.

Independent research or investigation resulting in a substantial formal report in the student's area of interest under the supervision of a faculty member.

Independent research or investigation resulting in a substantial formal report in the student's area of interest under the supervision of a faculty member.

This course showcases how networks are widespread in society, technology, and nature, via a mix of theory and applications. It demonstrates the importance of understanding network effects when making decisions in an increasingly connected world. Topics include an introduction to graph theory, game theory, social networks, information networks, strategic interactions on networks, network models, network dynamics, information diffusion, and more. Prerequisite: ORF 309 or permission of instructor. Two lectures, one precept.

Electronic commerce, traditionally the buying and selling of goods using electronic technologies, extends to essentially all facets of human interaction when extended to services, particularly information. The course focuses on both the software and the hardware aspects of traditional aspects as well as the broader aspects of the creation, dissemination and human consumption electronic services. Covered will be the physical, financial and social aspects of these technologies. Two lectures, one precept.

An introduction to popular statistical approaches in regression and time series analysis. Topics will include theoretical aspects and practical considerations of linear, nonlinear, and nonparametric modeling (kernels, neural networks, and decision trees). Prerequsites: ORF 245 and ORF 309 or instructor's permission. Two lectures, one lab, and one precept.

This is an introduction to the stochastic models inspired by the dynamics of resource sharing. Topics discussed include: early motivating communication systems (telephone and computer networks); modern applications (call centers, healthcare operations, and urban planning for smart cities); and key formulas (from Erlang blocking and delay to Little's law). We also review supporting stochastic theories like equilibrium Markov chains along with Markov, Poisson and renewal processes. Prerequisite: ORF 309 or equivalent.

An introduction to the uses of simulation and computation for analyzing stochastic models and interpreting real phenomena. Topics covered include generating discrete and continuous random variables, stochastic ordering, the statistical analysis of simulated data, variance reduction techniques, statistical validation techniques, nonstationary Markov chains, and Markov chain Monte Carlo methods. Applications are drawn from problems in finance, manufacturing, and communication networks. Students will be encouraged to program in Python. Office hours will be offered for students unfamiliar with the language. Prerequisites: ORF 245 and ORF 309.

This course develops several methods that are central to modern optimization and learning problems under uncertainty. These include dynamic programming, linear quadratic regulator, Kalman filter, multi-armed bandits and reinforcement learning. Representative applications and numerical methods are emphasized. Prerequisite: ORF 309. Two lectures.

This course covers the basic concepts of measuring, modeling and managing risks within a financial optimization framework. Topics include single and multi-stage financial planning systems. Implementation from several domains within asset management and goal based investing. Machine learning algorithms are introduced and linked to the stochastic planning models. Python and optimization exercises required. Prerequisites: ORF 245, ORF 309, ORF 335 or ECO 465 (concurrent enrollment is acceptable) or instructor's permission. Two lectures, one precept.

An introduction to the theory and practice of high frequency trading in modern electronic financial markets. We give an overview of the institutional landscape and basic empirical features of modern equity, futures, and fixed income markets. We discuss theoretical models for market making and price formation. Then we dig into detailed empirical aspects of market microstructure and how these can be used to construct effective trading strategies. Course work will be a mixture of theoretical and data-driven problems. Programming environment will be a mixture of the R statistical environment, with the Kdb database language.

This course is an introduction to commodities markets (energy, metals, agricultural products) and issues related to renewable energy sources such as solar and wind power, and carbon emissions. Energy and other commodities represent an increasingly important asset class, in addition to significantly impacting the economy and policy decisions. Emphasis will be on the term structure of commodity prices: behavior, models and empirical issues. Prerequisite: ORF 309 and ORF 335, or instructor permission. Two lectures, one precept.

Studied is the transportation sector of the economy from a technology and policy planning perspective. The focus is on the methodologies and analytical tools that underpin policy formulation, capital and operations planning, and real-time operational decision making within the transportation industry. Case studies of innovative concepts such as dynamic "value pricing", real-time fleet management and control, GPS-based route guidance systems, automated transit networks and the emergence of Smart Driving / Autonomous Cars. Prerequisite: ORF 245 or permission of instructor. Two lectures, one precept.

A course covering one or more advanced topics in operations research and financial engineering. Subjects may vary from year to year.

A course covering one or more advanced topics in operations research and financial engineering. Subjects may vary from year to year.

A formal report on research involving analysis, synthesis, and design, directed toward improved understanding and resolution of a significant problem. The research is conducted under the supervision of a faculty member, and the thesis is defended by the student at a public examination before a faculty committee. The senior thesis is equivalent to a year-long study and is recorded as a double course in the Spring.

A one-semester project that fulfills the departmental independent work requirement for concentrators. Topics are chosen by students in consultation with members of the faculty. A written report is required at the end of the term.

This foundational class is designed to introduce students to both the ideation and investigation components of research, with milestones guiding students towards a complete thesis in the spring semester. Classes will consist of presentations on research tools (including data, library, and computing resources), crash-courses in common research methodologies, and introduction to LaTeX for typesetting their final theses. Throughout the semester, students will discuss and present their thesis progress in smaller group settings. Past student theses will also be studied as examples.

A formal report on research involving analysis, synthesis, and design, directed toward improved understanding and resolution of a significant problem. The research is conducted under the supervision of a faculty member and the support of dedicated instructors and AIs. The thesis is submitted and defended by the student at a public examination before a faculty committee. This course completes the research work begun in the fall semester class ORF 498.