Operations Research and Financial Engineering Jump To: Jump To: Program Offerings B.S.E. Offering type B.S.E. Operations research and financial engineering may be considered as the modern form of a liberal education: modern because it is based on science, mathematics, computing and technology, and liberal in the sense that it provides for broad intellectual development and can lead to many different types of careers. By choosing judiciously from courses in engineering, science, mathematics, economics, public policy and liberal arts, each student may design a program adapted to their particular interests. All students start from a common academic core consisting of statistics, probability and stochastic processes, and optimization. Related courses focus on developing computing skills and exposing students to applications in a variety of sectors of the economy such as finance, mobility, logistics, energy, environment, health care, diversity, education and equity. All of these applications involve having humans in the loop and consequently confronting challenges of large data, large dimensions, risk, uncertainty, and the desire for good outcomes, the analytics of which are the focus of ORFE’s academic core. Students augment the core program with a coherent sequence of application-focused departmental electives. Students often draw on courses from economics, computer science, applied mathematics, civil and environmental engineering, mechanical and aerospace engineering, chemistry, molecular biology, psychology, sociology, and the Princeton School of Public and International Affairs. Requirements for study in the department follow the general requirements for the School of Engineering and Applied Science and the University. Goals for Student Learning Many real-world problems are tackled using the tools of statistics, probability and optimization. Statistics enables reasoned analysis of data, probability enables the creation of stochastic models that describe the data and its inherent randomness, while optimization enables meaningful decision-making under this quantified uncertainty. Statistics, Probability and Optimization, in that order of analysis, is central to training in ORFE, with applications in: Data science and machine learning, including deep learning, large-scale optimization, causal inference, biostatistics, policy evaluation, genomics, networks and graphical models, analysis of high-frequency time series and high-dimensional data. Decision science, control and learning, including service systems and queues, reinforcement learning, verification and learning of dynamical systems, optimal and stochastic control, robotics and autonomous systems, and large dynamic games. Finance and social sciences, including risk management, quantification of model uncertainty, optimal investment, mean field games, optimal contracting, econometrics, causal inference, program evaluation, public policy, decision and choice theory, energy and environmental finance, and reliability management of electricity grids. The focus on rigorous mathematical theory behind the applications provides ORFE graduates with intellectual flexibility. The emphasis on foundational theory in statistics, probability and optimization gives ORFE majors the versatility to address the challenges of the financial engineering and machine learning revolutions of the 21st century, and prepares them to tackle future societal challenges that involve data-driven decision-making. Program of Study The student's program is planned in consultation with the director of undergraduate studies and the student's adviser and requires a year-long thesis or a one-semester senior project. With departmental approval, the exceptional student who wishes to go beyond the science and engineering requirements may select other courses to replace some of the required courses in order to add emphasis in another field of engineering or science, or to choose more courses in the area of study. Suggested plans of study and areas of concentration are available from the director of undergraduate studies. In addition to the engineering school requirements, there are three components to the curriculum: The core requirements (four courses). These form the intellectual foundation of the field and cover statistics, probability, stochastic processes and optimization, along with more advanced courses in mathematical modeling. Departmental electives (ten courses). These are courses that either extend and broaden the core, or expose the student to a significant problem area or application closely related to the core program. Senior independent research. A full-year thesis (or a one-semester project plus an additional 400-level ORFE departmental) involving an application of the techniques in the program applied to a topic that the student chooses in consultation with a faculty adviser. Core requirements (four courses): ORF 245 Fundamentals of Engineering Statistics* ORF 307 Optimization ORF 309 Probability and Stochastic Systems ORF 335 Introduction to Financial Mathematics * Exam option: Prospective majors may apply to the department to sit for an exam in lieu of ORF 245. Majors who satisfy the ORF 245 requirement with the departmental exam must take an additional advanced statistics course as a departmental elective in its place. For more information about this option, please consult the department's website. Departmental electives (ten courses; if a one-semester project is selected in lieu of the senior thesis, an eleventh course is required): The departmental electives represent courses that further develop a student's skills in mathematical modeling either by a more in-depth investigation of core disciplines, applying these skills in specific areas of application, or by learning about closely related technologies. Students must choose ten courses, as appropriate, with the following constraints: There must be at least four courses from the Department of Operations Research and Financial Engineering (ORF). There can be no more than three courses from any one department (excluding ORF). A list of all other departmental electives may be found in the departmental undergraduate academic guide; see the department website. Additional Information Students in the department often participate in the following minor and certificate programs. Minor in Finance The department cooperates with the Bendheim Center for Finance, which offers a minor program in finance. Certificate Program in Optimization and Quantitative Decision Science The department sponsors a certificate program with the goal of developing quantitative skills for optimal decision- making in complex and uncertain environments. It is open to both ORFE and non-ORFE majors. Certificate in Applied and Computational Mathematics Students seeking a strong mathematical foundation can combine courses from the department with supporting courses that develop more fundamental mathematical skills. The department maintains research laboratories that may be used as part of undergraduate research projects. Princeton Autonomous Vehicle Engineering (PAVE) This extracurricular undergraduate activity focuses on the implementation of advanced sensing and control technologies for optimal autonomous decision-making in vehicles. The current objective is to assist in the actual deployment of advanced mobility systems, in particular making Trenton, New Jersey the world capital in the deployment of safe, equitable, sustainable, affordable, high-quality mobility for all. Financial Engineering Laboratory This facility provides students with access to specialized software packages and to financial data and news services. Research in the laboratory is concerned with the analysis of the various forms of financial risk and the development of new financial instruments intended to control the risk exposure of insurance and reinsurance companies. Faculty Chair Ronnie Sircar Director of Undergraduate Studies Alain L. Kornhauser Director of Graduate Studies Matias D. Cattaneo Professor Amir Ali Ahmadi René A. Carmona Matias D. Cattaneo Jianqing Fan Alain L. Kornhauser Sanjeev R. Kulkarni William A. Massey John M. Mulvey Ronnie Sircar Mete Soner Robert J. Vanderbei Associate Professor Mykhaylo Shkolnikov Ramon van Handel Assistant Professor Boris Hanin Emma Hubert Jason Matthew Klusowski Elizaveta Rebrova Bartolomeo Stellato Ludovic Tangpi Associated Faculty Yacine Aït-Sahalia, Economics Markus K. Brunnermeier, Economics Maria Chudnovsky, Mathematics Filiz Garip, Sociology Elad Hazan, Computer Science H. Vincent Poor, Electrical & Comp Engineering Jennifer Rexford, Provost Paul Seymour, Mathematics Allan M. Sly, Mathematics John D. Storey, Integrative Genomics Rocío Titiunik, Politics Wei Xiong, Economics Lecturer Margaret Holen Daniel Rigobon Daniel Scheinerman Visiting Lecturer Ioannis Akrotirianakis Robert Almgren Alex Dytso Michael Sotiropoulos For a full list of faculty members and fellows please visit the department or program website. Courses ORF 105 - The Science and Technology of Decision Making (also EGR 106) Not offered this year QCR 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. Staff ORF 245 - Fundamentals of Statistics (also EGR 245) Fall/Spring QCR 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 90 minute lectures, one precept. S. Kulkarni ORF 307 - Optimization (also EGR 307) Spring 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 90 minute lectures, one precept. B. Stellato ORF 309 - Probability and Stochastic Systems (also EGR 309/MAT 380) Fall/Spring 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, 216, or instructor's permission. Three lectures, one precept. R. van Handel ORF 311 - Stochastic Optimization and Machine Learning in Finance Spring 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. J. Mulvey ORF 322 - Human-Machine Interaction (also PSY 322) Not offered this year EC ORF 335 - Introduction to Financial Mathematics (also ECO 364) Spring QCR 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. Staff ORF 350 - Analysis of Big Data Spring QCR 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. Staff ORF 360 - Decision Modeling in Business Analytics Not offered this year This is an introductory course to decision methods and modeling in business and operations management. The course will emphasize both mathematical decision-making techniques, as well as popular data-based decision models arising from real applications. Upon completion of this course students will have learned analytical tools for modeling and optimizing business decisions. From a practical perspective, this will be a first course that gives an overview of advanced operations research topics including revenue management, supply chain management, network management, and pricing. Staff ORF 363 - Computing and Optimization for the Physical and Social Sciences (also COS 323) Fall/Spring QCR 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. Ahmadi ORF 374 - Special Topics in Operations Research and Financial Engineering Not offered this year A course covering special topics in operations research or financial engineering. Subjects may vary from year to year. Staff ORF 375 - Independent Research Project Fall 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. A. Kornhauser ORF 376 - Independent Research Project Spring 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. A. Kornhauser ORF 387 - Networks Spring 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. E. Rebrova ORF 401 - Electronic Commerce Spring 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 precept. A. Kornhauser ORF 405 - Regression and Applied Time Series Fall 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. J. Klusowski ORF 406 - Statistical Design of Experiments Not offered this year 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. Staff ORF 407 - Fundamentals of Queueing Theory Not offered this year QCR 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. Staff ORF 409 - Introduction to Monte Carlo Simulation Fall 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. W. Massey ORF 411 - Sequential Decision Analytics and Modeling (also ECE 411) Not offered this year 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 lectures, one precept. Staff ORF 417 - Dynamic Programming Not offered this year 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. Staff ORF 418 - Optimal Learning Fall QCR 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. E. Hubert ORF 435 - Financial Risk and Wealth Management Fall 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. L. Tangpi ORF 445 - High Frequency Markets: Models and Data Analysis Spring 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. R. Almgren ORF 455 - Energy and Commodities Markets (also ENE 455) Fall 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 lectures, one precept. R. Sircar ORF 467 - Transportation Systems Analysis Fall 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. Kornhauser ORF 473 - Special Topics in Operations Research and Financial Engineering Not offered this year A course covering one or more advanced topics in operations research and financial engineering. Subjects may vary from year to year. Staff ORF 474 - Special Topics in Operations Research and Financial Engineering Not offered this year A course covering one or more advanced topics in operations research and financial engineering. Subjects may vary from year to year. Staff ORF 478 - Senior Thesis Spring 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. Kornhauser ORF 497 - Senior Project 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. A. Kornhauser
