ORF 105 / EGR 106

The Science and Technology of Decision Making

Professor/Instructor

An individual makes decisions every day. In addition, other people are making decisions that have an impact on the individual. In this course we will consider both how these decisions are made and how they should be made. In particular, we will focus on the use of advanced computing and information technology in the decision-making process.

ORF 245 / EGR 245

Fundamentals of Statistics

Professor/Instructor

Jianqing Fan, Samory K. Kpotufe

A first introduction to probability and statistics. This course will provide the foundations of 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 real-world data sets. Prerequisite MAT 201 equivalent or concurrent.

ORF 307 / EGR 307

Optimization

Professor/Instructor

Robert Joseph Vanderbei

Many real-world problems involve maximizing a linear function subject to linear inequality constraints. Such problems are called Linear Programming (LP) problems. Examples include min-cost network flows, portfolio optimization, options pricing, assignment problems and two-person zero-sum games to name but a few. The theory of linear programming will be developed with a special emphasis on duality theory. Attention will be devoted to efficient solution algorithms. These algorithms will be illustrated on real-world examples such as those mentioned. Two 90 minute lectures, one preceptorial. Prerequisite MAT 202 or 204.

ORF 309 / EGR 309 / MAT 380

Probability and Stochastic Systems

Professor/Instructor

Ramon van Handel, Mykhaylo Shkolnikov

An introduction to probability and its applications. Random variables, expectation, and independence. Poisson processes, Markov chains, Markov processes, and Brownian motion. Stochastic models of queues, communication systems, random signals, and reliability. Three lectures, one preceptorial. Prerequisite: MAT 201 or instructor's permission.

ORF 311

Stochastic Optimization and Machine Learning in Finance

Professor/Instructor

John Michael Mulvey

This course covers the central topics of stochastic optimization with a focus on financial risk management and associated machine learning concepts. We discuss theory, computational issues, and successful applications of stochastic decision models, mostly for long-term financial planning problems. We solve large stochastic programs to assist with finding the "best" compromise solutions in the face of multiple and conflicting goals. There is attention to applications of machine learning concepts in financial planning systems. Prerequisites: ORF 307 or MAT 305, and 309. Two 90-minute classes, one preceptorial.

PSY 322 / ORF 322

Human-Machine Interaction

Professor/Instructor

Alain Lucien Kornhauser, Philip Nicholas Johnson-Laird, Joel Cooper

A multidisciplinary study of the fundamentals of human-machine interactions from both the human psychology/philosophy side and the machine engineering and design side. Philosophical, psychological, and engineering models of the human processor. Functional differences between people and machines, the nature of consciousness and intelligence, massively parallel computing and neural networks, and the concept of resonant synergism in human-machine interactions. Two 90-minute lectures; three laboratories during semester.

ORF 335 / ECO 364

Introduction to Financial Mathematics

Professor/Instructor

This course introduces the basics of quantitative finance, particularly the use of stochastic models to value and hedge risks from options, futures and other derivative securities. The models studied include binomial trees in discrete time, and the Black-Scholes theory is introduced in continuous-time models. Computational methods are introduced in Matlab. The second half of the class looks at modern topics such as credit risk, stochastic volatility, portfolio optimization, as well as lessons from the financial crisis. Prerequisites: ORF 309, ECO 100, and MAT 104. R. Sircar

ORF 350

Analysis of Big Data

Professor/Instructor

This course introduces statistical theory and methods for analyzing Big data, including massive data, high dimensional data, stream data, and network data. Topics include Sufficiency Principle, Divide-and-Conquer Principle, Bonferroni Principle, Parsimonious Principle, and Linear-Complexity Principle. Under a likelihood-based framework, three types of analysis are introduced, including Exploratory Analysis, Predictive Analysis, and Inferential Analysis. Example applications include image clustering and anomaly detection, text mining, computational advertisement, scientific data analysis, and data visualization.

ORF 363 / COS 323

Computing and Optimization for the Physical and Social Sciences

Professor/Instructor

Amir Ali Ahmadi

An introduction to several fundamental and practically-relevant areas of numerical computing with an emphasis on the role of modern optimization. Topics include computational linear algebra, descent methods, basics of linear and semidefinite programming, optimization for statistical regression and classification, trajectory optimization for dynamical systems, 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, finance, economics, control theory, and engineering.

ORF 374

Special Topics in Operations Research and Financial Engineering

Professor/Instructor

John Michael Mulvey

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

ORF 375

Independent Research Project

Professor/Instructor

Alain Lucien Kornhauser

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

ORF 376

Independent Research Project

Professor/Instructor

Alain Lucien Kornhauser

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

ORF 401

Electronic Commerce

Professor/Instructor

Alain Lucien Kornhauser

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 90-minute lectures, one 50-minute preceptorial.

ORF 405

Regression and Applied Time Series

Professor/Instructor

René A. Carmona

Statistical Analysis of financial data: Density estimation, heavy tail distributions and dependence. Regression: linear, nonlinear, nonparametric. Time series analysis: classical models (AR, MA, ARMA), state space systems and filtering, and stochastic volatility models (ARCH, GARCH). Prerequsites: ORF 245 and MAT 202.

ORF 406

Statistical Design of Experiments

Professor/Instructor

Major methods of statistics as applied to the engineering and physical sciences. The central theme is the construction of empirical models, the design of experiments for elucidating models, and the applications of models for forecasting and decision making under uncertainty. Three lectures. Prerequisite: 245 or equivalent.

ORF 407

Fundamentals of Queueing Theory

Professor/Instructor

William Alfred Massey

An introduction to the fundamental results of queuing theory. Topics covered include: the classical traffic, offered load, loss, and delay models for communication systems. The theory of Markov chains, Poisson processes, and renewal theory are discussed through concrete examples and motivations. Fundamental queuing results such as the Erlang blocking and delay formulae, Jackson networks, Little's law and Lindley's equation are presented. Applications are drawn from classical problems in voice and data network performance, to modern issues in healthcare operations. Prerequisite: ORF 309 or equivalent. Two 90-minute lectures.

ORF 409

Introduction to Monte Carlo Simulation

Professor/Instructor

William Alfred Massey

Introduction to the uses of simulation and computation in the analysis of stochastic models and interpreting real phenomena. Topics include generating discrete and continuous random variables, the statistical analysis of simulated data, variance reduction techniques, statistical validation techniques, stochastic ordering, nonstationary Markov chains, and Markov chain Monte Carlo methods. Applications are drawn from problems in finance, insurance, manufacturing, and communication networks. Students will be encouraged to program in Python. Precept offered to help students with the language. Prerequisite: ORF 309. Two 90-minute lectures.

ORF 411

Operations and Information Engineering

Professor/Instructor

Warren Buckler Powell

The management of complex systems through the control of physical, financial and informational resources. The course focuses on developing mathematical models for resource allocation, with an emphasis on capturing the role of information in decisions. The course seeks to integrate skills in statistics, stochastics and optimization using applications drawn from problems in dynamic resource management which tests modeling skills and teamwork. Prerequisites: ORF 245, ORF 307 and ORF 309, or equivalents. Two 90 minute lectures, preceptorial.

ORF 417

Dynamic Programming

Professor/Instructor

An introduction to stochastic dynamic programming and stochastic control. The course deals with discrete and continuous-state dynamic programs, finite and infinite horizons, stationary and nonstationary data. Applications drawn from inventory management, sequential games, stochastic shortest path, dynamic resource allocation problems. Solution algorithms include classical policy and value iteration for smaller problems and stochastic approximation methods for large-scale applications. Prerequisites: 307 and 309.

ORF 418

Optimal Learning

Professor/Instructor

Warren Buckler Powell

Addresses the problem of collecting information used to estimate statistics or fit a model which is then used to make decisions. Of particular interest are sequential problems where decisions adapt to information as it is learned. The course introduces students to a wide range of applications, demonstrates how to express the problem formally, and describes a variety of practical solution strategies. Prerequisite: ORF 245, ORF 309. Two 90-minute lectures, one preceptorial.

ORF 435

Financial Risk Management

Professor/Instructor

John Michael Mulvey

This course covers the basic concepts of modeling, measuring and managing different types of financial risks. Topics include portfolio optimization (mean-variance approach and expected utility), interest rate risk, pricing and hedging in complete and incomplete markets, indifference pricing, risk measures, systemic risk. Prerequisites: ORF 245, ORF 335 or ECO 465 (concurrent enrollment is acceptable) or instructor's permission. Two 90-minute lectures, one preceptorial.

ORF 455

Energy and Commodities Markets

Professor/Instructor

René A. Carmona

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 335 or instructor permission. Two 90 minute lectures, one precept.

ORF 467

Transportation Systems Analysis

Professor/Instructor

Alain Lucien Kornhauser

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. Two 90-minute lectures, one preceptorial.

ORF 473

Special Topics in Operations Research and Financial Engineering

Professor/Instructor

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

ORF 474

Special Topics in Operations Research and Financial Engineering

Professor/Instructor

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