Department of Operations Research and Financial Engineering

Faculty

Chair

  • Ronnie Sircar

Director of Undergraduate Studies

  • Alain L. Kornhauser

Director of Graduate Studies

  • Mykhaylo Shkolnikov

Professor

  • Amir Ali Ahmadi
  • René A. Carmona
  • Matias D. Cattaneo
  • Jianqing Fan
  • Alain L. Kornhauser
  • William A. Massey
  • John M. Mulvey
  • Warren B. Powell
  • Ronnie Sircar
  • Mete Soner
  • Robert J. Vanderbei

Associate Professor

  • Mykhaylo Shkolnikov
  • Ramon van Handel

Assistant Professor

  • Boris Hanin
  • Jason Klusowski
  • Miklos Z. Racz
  • Bartolomeo Stellato
  • Ludovic Tangpi

Associated Faculty

  • Yacine Aït-Sahalia, Economics
  • Markus K. Brunnermeier, Economics
  • Maria Chudnovsky, Mathematics
  • Weinan E, Mathematics
  • Sanjeev R. Kulkarni, Dean of the Faculty
  • H. Vincent Poor, Electrical Engineering
  • Paul Seymour, Mathematics
  • Yakov G. Sinai, Mathematics
  • John D. Storey, Integrative Genomics
  • Wei Xiong, Economics
For a full list of faculty members and fellows please visit the department or program website.

Program Information

Information and Departmental Plan of Study

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 his or her particular interests.

All students start from a common academic core consisting of statistics, probability and stochastic processes, and optimization. Related courses focus on developing computer skills and exposing students to applications in areas such as finance, operations, transportation, and logistics. Students augment the core program with a coherent sequence of departmental electives. Students may also design specialized programs in areas such as medicine and neuroscience, which must be reviewed and approved by their academic adviser and the departmental representative. Students often draw on courses from economics, computer science, applied mathematics, civil and environmental engineering, mechanical engineering, chemistry, molecular biology, psychology, 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.

Program of Study

The student's program is planned in consultation with the departmental representative 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 departmental representative.

In addition to the engineering school requirements, there are three components to the curriculum:

1. 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.

2. 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.

3. 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

Departmental electives (ten courses, if a one-semester project is selected but not usually recommended): 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:

1. There must be at least four courses from the Department of Operations Research and Financial Engineering (ORF).

2. 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.

Students in the department often participate in the following certificate programs and laboratories:

Certificate in Finance. The department cooperates with the Bendheim Center for Finance, which offers a certificate program in finance.

Certificate Program in Engineering and Management Systems. The department sponsors a certificate program for students majoring in other departments who complete a significant part of the core of the undergraduate program.

Certificate in Applied and Computational Mathematics. Students seeking a strong mathematical foundation can combine courses from the department with supporting courses which develop more fundamental mathematical skills.

The department maintains several research laboratories which 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 the development of an autonomous vehicle that can pass the New Jersey State Driving Test.

Princeton Laboratory for Energy Systems Analysis. PENSA is the home of the SAP Initiative for Energy Systems Research at Princeton University. Our goal is to bring advanced analytical thinking to the development of new energy technologies, the rigorous study of energy policy, and the efficient management of energy resources.

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.

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. Instructed by: 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 equivalent or concurrent. Two 90 minute lectures, one preceptorial. Instructed by: R. Pereira Masini, M. Cattaneo

ORF 307 Optimization (also
EGR 307
) Spring

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. Instructed by: R. Vanderbei

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. Three lectures, one precept. Prerequisite: MAT 201 or instructor's permission. Instructed by: M. Shkolnikov, 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 309. Two 90-minute classes, one preceptorial. Instructed by: J. Mulvey

ORF 322 Human-Machine Interaction (See PSY 322)

ORF 335 Introduction to Financial Mathematics (also
ECO 364
) Spring QCR

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. Instructed by: M. Soner

ORF 350 Analysis of Big Data Spring QCR

The amount of data in our world has been exploding and analyzing large data sets is a central challenge in society. This course introduces the statistical principles and computational tools for analyzing big data. Topics include statistical modeling and inference, model selection and regularization, scalable computational algorithms, and more. Prerequisite: ORF 245, ORF 309. Lecture and precept. Instructed by: B. Hanin

ORF 360 Decision Modeling in Business Analytics Spring

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. Instructed by: M. Wang

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 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. A. Ahmadi, Instructed by: Staff

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. Instructed by: J. Mulvey

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. Instructed by: 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. Instructed by: A. Kornhauser

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 preceptorial. Instructed by: A. Kornhauser

ORF 405 Regression and Applied Time Series Fall

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. Instructed by: L. Tangpi

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. Instructed by: Staff

ORF 407 Fundamentals of Queueing Theory Spring 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. Instructed by: 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.Prerequisite: ORF 309. Instructed by: M. Soner

ORF 411 Sequential Decision Analytics and Modeling (also
ELE 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 90 minute lectures, preceptorial. Instructed by: 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. Instructed by: Staff

ORF 418 Optimal Learning Not offered this year QCR

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. Instructed by: Staff

ORF 435 Financial Risk and Wealth Management Fall

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. Instructed by: J. Mulvey

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 90 minute lectures, one precept. Instructed by: 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. Two 90-minute lectures, one preceptorial. Instructed by: A. Kornhauser

ORF 473 Special Topics in Operations Research and Financial Engineering Spring

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

ORF 474 Special Topics in Operations Research and Financial Engineering Spring

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

ORF 479 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. Instructed by: A. Kornhauser