Department of Operations Research and Financial Engineering
Faculty
Chair Director of Graduate Studies Professor Associate Professor Assistant Professor |
Assistant Professor (continued) Associated Faculty
Yacine Aït-Sahalia, Economics Markus K. Brunnermeier, Economics Weinan E, Mathematics Christodoulos A. Floudas, Chemical and Biological Engineering Sanjeev R. Kulkarni, Electrical Engineering H. Vincent Poor, Electrical Engineering Robert E. Schapire, Computer Science José A. Scheinkman, Economics Paul D. Seymour, Mathematics Christopher Sims, Economics
Yakov G. Sinai, Mathematics John D. Storey, Molecular Biology and Lewis-Sigler Institute for Integrative Genomics Wei Xiong, Economics |
Requirements
The department offers two degree programs: the Doctor of Philosophy (Ph.D.) in operations research and financial engineering, and a Master of Science in Engineering (M.S.E. These programs provide a great deal of flexibility for students in designing individual plans of study and research according to their needs and interests. The department is a major participant in the Master of Finance (M.Fin.) program offered through the Bendheim Center for Finance and in participation with the Department of Economics.
All students are admitted as candidates for the Ph.D. or MSE. There is no separate M.A. program. Students may apply for the award of the M.A. as an incidental degree after passing the Ph.D. general examination or as a terminal degree for those withdrawing from the programs. An ad hoc committee will be formed to consider the applications from those withdrawing from the programs
Admission Requirements
A bachelor’s degree in engineering, sciences, or mathematics is normally required for admission to the graduate program. Applicants should submit the results of the Graduate Record Examination (GRE). The Mathematics Subject Test is strongly recommended. International students from non-English-speaking countries, whose bachelor’s degrees are not from an English-language institution, should also submit the results of the Test of English as a Foreign Language (TOEFL) or IELTS.
Master of Science in Engineering
The ORFE department is geared towards educating students whose ultimate goal is to get a Ph.D. The admission rate for the M.S.E. degree is very low. Applicants interested in an M.S.E. degree from ORFE are urged to identify and contact a faculty member in whose area of research they would like to work. Admission will be based on not only qualifications of applicant, but also requires support of at least one faculty member who expresses an interest to supervise the applicant. Students enrolled in this program are eligible for financial support in the form of research or teaching assistantships if such funds are available. Applicants who are primarily interested in a Master's degree in Finance should apply for the Master in Finance at the Bendheim Center for Finance. The School of Engineering provides more information regarding the Master of Science in Engineering program.
The ORFE department is geared towards educating students whose ultimate goal is to get a Ph.D. The admission rate for the M.S.E. degree is very low. Applicants interested in an M.S.E. degree from ORFE are urged to identify and contact a faculty member in whose area of research they would like to work. Admission will be based on not only qualifications of applicant, but also requires support of at least one faculty member who expresses an interest to supervise the applicant. Students enrolled in this program are eligible for financial support in the form of research or teaching assistantships if such funds are available. Applicants who are primarily interested in a Master's degree in Finance should apply for the Master in Finance at the Bendheim Center for Finance. The School of Engineering provides more information regarding the Master of Science in Engineering program.
The M.S.E. program has a strong research focus reflected in the requirement of a thesis. The course requirements are fulfilled by successfully completing ten one-semester courses, two of which are required research courses (ORF 509 and 510). The M.S.E. degree is usually completed within two academic years of full-time study.
Doctor of Philosophy
The plan of study for the first year is prepared by the student in consultation with an informal faculty adviser and the director of graduate studies. A typical plan consists of six courses, emphasizing the foundations of the program.
The plan of study for the first year is prepared by the student in consultation with an informal faculty adviser and the director of graduate studies. A typical plan consists of six courses, emphasizing the foundations of the program.
By the end of the first year, the student is expected to narrow his or her area of doctoral research and choose an appropriate adviser. The second year of study starts with a qualifying examination and is spent with advanced course work, research projects, and preparation for the general examination. The general examination is normally taken at the end of the second year.
Beyond the general examination, the completion of a dissertation usually takes two to three years. Upon acceptance of the dissertation by the department, the candidate for the Ph.D. takes the final public oral examination, which is primarily a defense of the dissertation.
Qualifying Examination
Each student must satisfy qualifying requirements in the areas of 4 of the 6 core classes.
Qualifying exams in these areas will be offered in September of the student’s second year.
If a student’s grade in a core course taken in the first year is A- or better, the student is exempt from taking the qualifying exam in that area. Before the exam, the student must have acquired demonstrated competence in real analysis at the level of MATH 314.
The optimization exams are based on ORF 522 and ORF 523. The probability exams are based on ORF 526 and ORF 527. The statistics exams are based on ORF 524 and ORF 525.
General Examination
ORFE students take the general exam in April or May of their second year. By that time, the students have met the qualifying examination requirements, have taken and passed ORF 509, have taken or are currently enrolled in ORF 510 and have passed with a B+ or higher two advanced courses. The student must have shown adequate progress on research and an acceptable level of understanding of his or her area of specialization.
ORFE students take the general exam in April or May of their second year. By that time, the students have met the qualifying examination requirements, have taken and passed ORF 509, have taken or are currently enrolled in ORF 510 and have passed with a B+ or higher two advanced courses. The student must have shown adequate progress on research and an acceptable level of understanding of his or her area of specialization.
The general exam consists of two parts, a written and an oral part, both covering the students primary area of specialization. The written part requires taking and passing with a B+ or higher two approved advanced courses at the graduate (500) level beyond the 4 core classes counted for the Qualifying Exam. These two courses must be approved by the student’s advisor and the DGS.
For each student, an examining committee is selected by the student and advisor. It has to be approved by the Director of Graduate Studies. The committee consists of the student’s advisor and two additional ORFE faculty or affiliated faculty. The committee will administer the oral exam, evaluate the student’s performance in research and overall knowledge of his/her field, and make a recommendation to the department faculty. A departmental faculty vote determines the final outcome. The oral exam may be up to 3 hours in length.
Information on the oral exam: Before the exam, the student is required to submit a comprehensive written report on the research conducted in ORF 509-510. It is due one week before the exam takes place. The report serves as the basis for the student’s presentation. The purpose of the presentation is to explain the research the student has done so far and plans to do in the future. Examining faculty may ask questions on the presentation and on any other material deemed appropriate for a comprehensive examination.
Areas of Study and Research
Each doctoral program is formulated to prepare students for research and teaching. The aim of the program is to provide a strong methodological background, coupled with significant competence in some area of application. The emphasis is on the conceptual foundations, mathematical models of real phenomena, and computational issues in practical problem solving.
Each doctoral program is formulated to prepare students for research and teaching. The aim of the program is to provide a strong methodological background, coupled with significant competence in some area of application. The emphasis is on the conceptual foundations, mathematical models of real phenomena, and computational issues in practical problem solving.
Current teaching and research activities include probability and stochastic processes, linear and nonlinear optimization, statistics and machine learning, coupled to applications in finance and economics, energy and the environment, transportation, risk measurement and management, astrophysics, biostatistics, big data analysis, among others.
Interdisciplinary Programs
The departmental faculty are affiliated with a number of interdisciplinary programs and centers: the Andlinger Center for Energy and the Environment, the Program in Applied and Computational Mathematics, the Graduate Program in Quantitative and Computational Biology, the Princeton Environmental Institute, the Princeton Neuroscience Institute, the Program in Robotics and Intelligent Systems, and the Bendheim Center for Finance. Students may combine their departmental work with courses and research opportunities offered by such programs and centers and also by the departments of computer science, economics, and mathematics.
The departmental faculty are affiliated with a number of interdisciplinary programs and centers: the Andlinger Center for Energy and the Environment, the Program in Applied and Computational Mathematics, the Graduate Program in Quantitative and Computational Biology, the Princeton Environmental Institute, the Princeton Neuroscience Institute, the Program in Robotics and Intelligent Systems, and the Bendheim Center for Finance. Students may combine their departmental work with courses and research opportunities offered by such programs and centers and also by the departments of computer science, economics, and mathematics.
Colloquium and Research Seminars
The departmental colloquium and seminar series brings distinguished researchers and practitioners from other universities and businesses to present their latest work. In addition, informal research seminars are organized in order to exchange information and to discuss ideas arising from the research work in progress. Students, research staff, visiting scholars, and faculty members participate in these seminars.
The departmental colloquium and seminar series brings distinguished researchers and practitioners from other universities and businesses to present their latest work. In addition, informal research seminars are organized in order to exchange information and to discuss ideas arising from the research work in progress. Students, research staff, visiting scholars, and faculty members participate in these seminars.
Fellowships and Assistantships
The department aims to support all doctoral students requesting aid through a combination of fellowships and assistantships. All first-year Ph.D. candidates are supported by full-time fellowships, allowing students to focus on courses and providing flexibility in the choice of a research advisor. From the second year onward, students are supported by a combination of teaching assistantships, research assistantships, and fellowships. Continuation of support is recommended on the basis of satisfactory progress.
The department aims to support all doctoral students requesting aid through a combination of fellowships and assistantships. All first-year Ph.D. candidates are supported by full-time fellowships, allowing students to focus on courses and providing flexibility in the choice of a research advisor. From the second year onward, students are supported by a combination of teaching assistantships, research assistantships, and fellowships. Continuation of support is recommended on the basis of satisfactory progress.
Further details on financial support can be found on the Graduate School website.
Courses
Operations Research and Financial Engineering
ORF 504/FIN 504 Financial Econometrics
Professor Jianqing Fan
This course covers econometric and statistical methods as applied to finance. Topics include a sset returns and efficient market hypothesis, linear time series, discrete time volatility models, efficient portolios and CAPM, multifactor pricing models, portfolio allocation and risk assessment, intertemporal equilibrium models, present value models, simulation methods for financial derivatives, and econometrics of continuous time finance.
ORF 505/FIN 505 Modern Regression and Time Series
René A. Carmona
Heavy tailed distributions and copulas. Simple and multiple linear regressions. Nonlinear regression. Nonparametricegression and classification. Time series analysis: stationarity and classical linear models (AR, MA, ARMA). Nonlinear and nonstationary time series models. State space systems, hidden Markov models and filtering.
ORF 507 Master's Project I
Staff
ORF 507 Master's Project I
Staff
Under the direction of a faculty member, each student carries out a master's project, writes a report, and presents the results. Master's project I is usually taken during the fall semester of the Master of Engineering program; master's project II is taken during spring.
ORF 508 Master's Project II
Staff
ORF 508 Master's Project II
Staff
Under the direction of a faculty member, each student carries out a master's project, writes a report, and presents the results. Master's project I is usually taken during the fall semester of the Master of Engineering program; master's project II is taken during spring.
ORF 509 Directed Research I
Staff
ORF 509 Directed Research I
Staff
Under the direction of a faculty member, Ph.D. and M.S.E. students carry out research, write a report each, and present the results. Directed Research I is normally taken during the first year of study.
ORF 510 Directed Research II
Staff
Under the direction of a faculty member, Ph.D. and M.S.E. students carry out research, write a report each, and present the results. Of these, 509 is normally taken during the first year of study. Doctoral students should complete 510 in the fall term of their second year.
ORF 511 Extramural Summer Project
Director Of Graduate Studies (DGS)
ORF 511 Extramural Summer Project
Director Of Graduate Studies (DGS)
Summer research project designed in conjunction with the student's advisor and an industrial, NGO, or government sponsor, that will provide practical experience relevant to the student's course of study. Start date no earlier than June 1. A research report and sponsor's evaluation are required.
ORF 515/FIN 503 Asset Pricing II: Stochastic Calculus and Advanced Derivatives
Birgit Rudloff
ORF 515/FIN 503 Asset Pricing II: Stochastic Calculus and Advanced Derivatives
Birgit Rudloff
Course covers the pricing and hedging of advanced derivatives, including topics such as exotic options, greeks, interest rate derivatives and credit derivatives, as well as covering the basics of stochastic calculus necessary for finance. Designed for Masters students.
ORF 522 Linear and Convex Optimization
Robert J. Vanderbei
ORF 522 Linear and Convex Optimization
Robert J. Vanderbei
Topics discussed include: the simplex method and its complexity, degeneracy, duality, the revised simplex method, convex analysis, game theory, network flows, primal-dual interior point methods, first order optimality conditions, Newton's method, KKT conditions, quadratic programming, and convex optimization. A broad spectrum of applications are presented.
ORF 523 Advanced Optimization
Sebastien Bubeck
ORF 523 Advanced Optimization
Sebastien Bubeck
A mathematical introduction to large-scale optimization and stochastic optimization. Topics covered include the analysis of diverse gradient-descent algorithms such as sub-gradient descent, Nesterov's accelerated gradient descent, FISTA and mirror descent, as well as a discussion of complexity lower bounds à la Nemirovski. These methods will be compared to the semi-definite programming approach and applications to high-dimensional statistics and machine learning will also be discussed.
ORF 524 Statistical Theory and Methods
Philippe Rigollet
ORF 524 Statistical Theory and Methods
Philippe Rigollet
A graduate-level introduction to statistical theory and methods and some of the most important and commonly-used principles of statistical inference. Covers the statistical theory and methods for point estimation, confidence intervals, and hypothesis testing.
ORF 525 Statistical Learning and Non-Parametric Estimation
Philippe Rigollet
ORF 525 Statistical Learning and Non-Parametric Estimation
Philippe Rigollet
A theoretical introduction to statistical learning problems related to regression and classification. Topics covered include: Principle Component Analysis, nonparametric estimation, sparse regression, and Classification and Statistical learning
ORF 526 Probability Theory
Patrick Cheridito
ORF 526 Probability Theory
Patrick Cheridito
Graduate introduction to probability theory beginning with a review of measure and integration. Topics include random variables, expectation, characteristic functions, law of large numbers, central limit theorem, conditioning, martingales, Markov chains, and Poisson processes
ORF 527 Stochastic Calculus
Ramon van Handel
ORF 527 Stochastic Calculus
Ramon van Handel
An introduction to stochastic calculus based on Brownian motion.Topics include:construction of Brownian motion; martingales in continuous time; the Ito integral; localization; Ito calculus; stochastic differential equations; Girsanov's theorem; martingale representation; Feynman-Kac formula.
ORF 531/FIN 531 Computational Finance in C++
Staff
ORF 531/FIN 531 Computational Finance in C++
Staff
The intent of this course is to introduce the student to the technical and algorithmic aspects of a wide spectrum of computer applications currently used in the financial industry, and to prepare the student for the development of new applications. The student will be introduced to C++, the weekly homework will involve writing C++ code, and the final project will also involve programming in the same environment.
ORF 533 Convex Analysis for Mathematical Finance
Birgit Rudloff
ORF 533 Convex Analysis for Mathematical Finance
Birgit Rudloff
Tools from Convex Analysis are studied in the context of Mathematical Finance and economics, including the Hahn-Banach theorem, Legendre-Fenchel transforms, biconjugation theorem, subdifferentials, and duality. As a main application, translation invariant functions such as risk measures, no-arbitrage price bounds, good deal bounds, benefit functions and optimized certainty equivalents, are studied. Further applications include the Fundamental Theorem of Asset Pricing, hedging problems, capital/risk allocation and utility maximization.
ORF 534 Quantitative Investment Science
John M. Mulvey
ORF 534 Quantitative Investment Science
John M. Mulvey
A survey of central topics in the area of investment management and financial planning. Integrating pricing methodologies with financial planning models. Linking asset and liability strategies to achieve investment goals and meet liabilities. We model the enterprise as a multi-stage stochastic program with decision strategies.
ORF 535/FIN 535 Financial Risk Management
Birgit Rudloff
This course covers the basic concepts of modeling, measuring and managing financial risks. Topics include portfolio optimization (mean variance approach and expected utility), interest rate risk, pricing and hedging in incomplete markets, indifference pricing, risk measures, systemic risk.
ORF 538 PDE Methods for Financial Math
Ronnie Sircar
An introduction to analytical and computational methods common to financial engineering problems. Aimed at PhD students and advanced masters students who have studied stochastic calculus, the course focuses on uses of partial differential equations: their appearance in pricing financial derivatives, their connection with Markov processes, their occurrence as Hamilton-Jacobi-Bellman equations in stochastic control problems, and analytical, asymptotic, and numerical techniques for their solution.
ORF 542 Stochastic Control and Stochastic Differential Games
René A. Carmona
René A. Carmona
Review of (forward) stochastic differential equations. Introduction to Backward Stochastic Differential Equations (BSDE's). Stochastic control=dynamic programming, HJB equations and connection with BSDE's. Stochastic differential games=Nash equilibriums. Isaacs condition and BSDE's. Applications of stochastic control and stochastic games to recent research results in Finance.
ORF 551/APC 551 random Measures and Levy Processes
Erhan Çinlar
ORF 551/APC 551 random Measures and Levy Processes
Erhan Çinlar
Poisson random measures, additive measures, Poisson-Dirichlet processes, self-exciting point processes; Levy processes, Ito-Levy characterization; subordination, subordinators, and stable processes.
ORF 554 Markov Processes
Erhan Çinlar
ORF 554 Markov Processes
Erhan Çinlar
Markov processes with general state spaces; transition semigroups, generators, resolvants; hitting times, jumps, and Levy systems; additive functionals and random time changes; killing and creation of Markovian motions.
ORF 557 Stochastic Analysis Seminar
René A. Carmona
ORF 557 Stochastic Analysis Seminar
René A. Carmona
Recent developments in the theory and applications of the analysis of random processes and random fields. Applications include financial engineering, transport by stochastic flows, and statistical imaging.
ORF 558 Stochastic Analysis Seminar
Staff
ORF 558 Stochastic Analysis Seminar
Staff
Recent developments in the theory and applications of the analysis of random processes and random fields. Applications include financial engineering, transport by stochastic flows, and statistical imaging.
ORF 565 Empirical Processes and Asymptotic Theory
ORF 565 Empirical Processes and Asymptotic Theory
Jianqing Fan
Empirical Process theory mainly extends the law of large numbers (LLN), central limit theorem (CLT) and exponential inequalities to uniform LLN's and CLT's and concentration inequalities. This uniformaty is useful to statisticians and computer scientists in that they often model data as a sample from some unknown distribution and desire to estimate certain aspects of the population. Uniform LLN or CLT and concentration inequalities will imply that certain sample averages will be uniformly close to their expectations regardless of the unknown distributions. This class intends to review modern empirical process theory and its related asymptotics.
ORF 569 Special Topics in Statistics and Operations Research
Staff
Advanced topics in statistics and operations research or the investigation of problems of current interest.
ORF 570 Special Topics in Statistics and Operations Research
Staff
ORF 570 Special Topics in Statistics and Operations Research
Staff
Advanced topics in statistics and operations research or the investigation of problems of current interest.
ORF 574/FIN 574 Special Topics in Investment Science
John M. Mulvey
ORF 574/FIN 574 Special Topics in Investment Science
John M. Mulvey
Emphasis on quantitative analysis of markets, trading strategies, risk and return profiles and portfolio analysis. Students develop portfolios of hedge funds; analyze trading models for various hedge fund styles; develop Value-at-Risk analysis of various trading systems and portfolios; analyze relationship between macro-economic variables and various hedge fund trading strategies; analyze hedge funds from the standpoint of asset allocation and efficient frontier models. We will also bring in experts and practitioners in a number of hedge fund trading strategies to add industry feel and context to the lectures and exercises.
ORF 575 Financial Engineering Seminar
Ronnie Sircar
ORF 575 Financial Engineering Seminar
Ronnie Sircar
Discussion of recent topics and papers in financial mathematics.