Department of Operations Research and Financial Engineering

Chair

Robert J. Vanderbei

Director of Graduate Studies

Warren B. Powell

Professor

René A. Carmona

Erhan Çinlar

Jianqing Fan

Alain L. Kornhauser

William A. Massey

John M. Mulvey

Warren B. Powell

Robert J. Vanderbei

Visiting Professors

Roger Burk

Richard De Veaux

Marc Hallin

Associate Professor

K. Ronnie Sircar

Assistant Professor

Patrick Cheridito

Alexandre W. d’Aspremont

Savas Dayanik

Victoria Henderson

Associated Faculty

Yacine Ait-Sahalia, Economics

Ingrid C. Daubechies, Mathematics

Avinash K. Dixit, Economics

Christodoulos A. Floudas, Chemical Engineering

Sanjeev R. Kulkarni, Electrical Engineering

H. Vincent Poor, Electrical Engineering

José A. Scheinkman, Economics

Stuart C. Schwartz, Electrical Engineering

 

The department offers three degree programs: the Doctor of Philosophy (Ph.D.) in Operations Research and Financial Engineering, a Master of Science in Engineering (M.S.E.), and a one-year Master of Engineering (M.Eng.). 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.) degree program offered through the Bendheim Center for Finance and in participation with the Department of Economics.

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). 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.

Further information than that given below may be obtained via our Web page at www.orfe.princeton.edu.

Master of Engineering

The M.Eng. degree program has been developed to meet the need for advanced training in the applied aspects of modern engineering. Program requirements are met by successfully completing eight graduate-level courses from a list relevant to the field. A thesis is not required. Normally, the program can be completed in one academic year of full-time study. Part-time status is available for qualified students. Financial support is normally not available.

This M.Eng. program is for students whose main interests are in operations research. A typical program of study consists of courses in statistics, stochastic calculus, and optimization as well as four electives. Master’s projects are available as electives. Students who are primarily interested in a master’s degree in financial engineering should apply to the Master of Finance degree program available through the Bendheim Center for Finance.

Master of Science in Engineering

The M.S.E. program requires 10 courses, two of which are research courses, as well as a master’s thesis. These requirements are typically completed over a two-year period. Courses may be chosen from within the department or any of a number of related departments, in consultation with the director of graduate studies.

Students should not apply to the M.S.E. program if they are interested in subsequently obtaining a Ph.D. Master’s-degree students are generally not provided financial support. As the graduate program is primarily directed toward doctoral research, students interested in a master’s degree are encouraged to contact the director of graduate studies before submitting an application.

Doctor of Philosophy

Upon admission to the Ph.D. program, each student is assigned an adviser in his or her area of interest. The plan of study for the first year is prepared by the student in consultation with the adviser and the director of graduate studies. A typical plan consists of eight 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 to lead it. 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.

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 disciplinary 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, optimal stochastic control, dynamic and stochastic programming, stochastic differential equations and stochastic flows, statistics and calibration of stochastic models, statistical signal and image analysis, trajectory optimization, dynamic resource management, and transportation and equilibrium analysis. A particular area of interest is financial engineering: stochastic calculus for finance, models of stochastic volatility and insider information, statistical and computational aspects of finance, and risk analysis and management.

Interdisciplinary Programs

The departmental faculty are affiliated with a number of interdisciplinary programs and centers: the Program in Applied and Computational Mathematics, the Program in Transportation, 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.

Research Seminars

The departmental 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. The fellowships vary in amount and detailed provisions. The amounts of financial assistance through assistantships are fixed, as indicated in the general section on awards and financial assistance in this catalog.

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 adviser. Beginning with the second year, students are supported by a combination of teaching assistantships, research contracts, and fellowships. Continuation of support is recommended on the basis of satisfactory progress.

Equipment and Facilities

The department offers a wide range of facilities for computer-based research. These include the following:

Computational and Stochastic Transportation and Logistics Engineering (CASTLE) Laboratory. Activities focus on a broad range of dynamic asset-management problems, ranging from managing transportation equipment (trucks, trains, and planes), asset acquisition problems (equipment for the electric power industry), and related pricing problems. Emphasis is on the development of computational methods for stochastic optimization using the techniques of approximate dynamic programming. Students gain access to developmental libraries, diagnostic tools, and a vast array of data from industrial applications.

Financial Engineering Laboratory. This laboratory holds the computers, software, and financial data feeds needed for teaching and research in financial engineering. It is a focal point for graduate students in the Ph.D. program in financial engineering and M.Fin. It also serves as a gateway to collaborative research projects with financial institutions.

Optimization Tools and Models (OPTOMO) Library. This library is an Internet-based library that provides students with access to a large collection of important real-world optimization models together with state-of-the-art tools for solving them.

Statistics lab. Research emphasizes developing statistical theory and methods arising from various disciplines of science and engineering where quantitative analysis plays an important role. The lab focuses particularly on financial econometrics and risk management, bioinformatics and biostatistics, and machine learning, but it has genuine interests in confronting statistical problems that arise in a broad range of problems. The statistics lab also conducts research into the development of data-analytic nonparametric and semi-parametric techniques, and provides fundamental theory to understand the techniques in use that push theory, methods, and applications forward.

Transportation Information and Decision Engineering (TIDE) Center. The center conducts research on information and decision engineering technologies and how these technologies can be used to improve transportation-related decision making. It is a cooperative effort involving Princeton University, the New Jersey Institute of Technology, and Rutgers University and is sponsored by the New Jersey Commission on Science and Technology under its R&D Excellence Program.

Courses

ORF 504 Financial Econometrics (also FIN 504)

Jianqing Fan

Covers econometric and statistical methods as applied to finance. Topics include measurement issues in finance, predictability of asset returns and volatilities, value at risk and extremal events, linear-factor pricing and portfolio problems, intertemporal models of the Stochastic Discount Factor and Generalized Method of Moments, vector autoregressive and maximum likelihood methods in finance, risk neutral valuation in discrete time, estimation methods for continuous-time models, volatility smiles and alternatives to Black-Scholes, and nonparametric statistical methods for option pricing.

ORF 505 Modern Regression and Time Series (also FIN 505)

René A. Carmona

Linear and mixed-effect models. Nonlinear regression. Nonparametric regression 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, 508 Master’s Project I, 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 the spring.

ORF 509, 510 Directed Research I, II

Staff

Under the direction of a faculty member, Ph.D. and M.S.E. students carry out research, write a report, and present the results. Of these, ORF 509 is normally taken during the first year of study. Doctoral students should complete ORF 510 one semester prior to taking the general examination.

ORF 511 Extramural Summer Project

Staff

Summer research project designed in conjunction with the student’s adviser and an industrial, NGO, or government sponsor that provides practical experience relevant to the student’s course of study. The start date is no earlier than June 1. A research report and sponsor’s evaluation are required.

ORF 514 Asset Pricing I: Pricing Models and Derivatives (see FIN 501)

ORF 515 Asset Pricing II: Stochastic Calculus and Advanced Derivatives (also FIN 503)

Alexandre W. d’Aspremont, Victoria Henderson

Begins with an overview of basic probability theory and covers the elements of stochastic calculus and stochastic differential equations that are widely used in derivatives modeling, pricing, and hedging. Topics include Brownian motion, martingales, and diffusions and their uses in stochastic volatility; volatility smiles; risk management; interest-rate models; and derivatives, swaps, credit risk, and real options.

ORF 518 Applied Stochastic Analysis and Methods (see APC 518)

ORF 522 Linear Optimization

Robert J. Vanderbei

Theoretical concepts underlying linear programming, with computer implementations of some of the different methods. Topics covered include duality theory, the simplex method, interior point methods, related numerical issues, and modeling paradigms.

ORF 523 Nonlinear Optimization

Alexandre W. d’Aspremont

An introduction to the central concepts needed for studying the theory, algorithms, and applications of nonlinear optimization problems. Topics covered include first- and second-order optimality conditions; unconstrained methods, including steepest descent, conjugate gradient, and quasi-Newtonian methods; constrained active-set methods; and duality theory and Lagrangian methods. Prerequisite: ORF 522.

ORF 524 Statistical Theory and Methods

Jianqing Fan

A graduate-level introduction to statistical theory and methods. Introduces some of the most important and commonly used principles of statistical inference and covers the statistical theory and methods for point estimation, confidence intervals, hypothesis testing, and the applications of the fundamental theory to linear models and categorical data.

ORF 526 Stochastic Modeling

Erhan Çinlar, Savaş Dayanik

Fundamental models of random phenomena in engineering and operations research, including Poisson processes, Markov chains, renewal processes, and Brownian motion.

ORF 527 Stochastic Calculus and Finance

Patrick Cheridito

An introduction to stochastic analysis based on Brownian motion. Topics include local martingales, the Ito integral and calculus, stochastic differential equations, the Feynman-Kac formula, representation theorems, Girsanov theory, and applications in finance.

ORF 530 Financial Data Mining

Sanjeev R. Kulkarni

The purpose is to introduce students to modern techniques in pattern recognition and data analysis useful in the processing of financial data.

ORF 531 Computational Finance in C++ (also FIN 531)

René A. Carmona

Introduces students to the technical and algorithmic aspects of a wide spectrum of computer applications currently used in the financial industry, preparing them for the development of new applications. Students are introduced to C++, the weekly homework involves writing C++ code, and the final project also involves programming in the same environment.

ORF 534 Financial Engineering (also FIN 534)

John M. Mulvey

A survey of central topics in the area of financial engineering and multiperiod financial planning systems. Pricing methodologies integrated with financial planning systems. Linking asset and liability strategies to maximize surplus-wealth over time. We model the organization as a multistage stochastic program, with decision strategies.

ORF 535 Financial Risk Management (also FIN 535)

Patrick Cheridito

This course is about measuring, modeling, and managing financial risks. It introduces the variety of instruments that are used to this effect, and the methods of designing and evaluating such instruments. Topics covered include risk diversification, planning models, market and nonmarket risks, and portfolio effects.

ORF 538 Analytical and Computational Methods for Financial Engineering

Ronnie Sircar

This class introduces analytical and computational methods that are common in financial engineering problems. It is aimed at Ph.D. students and advanced M.A. students who have studied stochastic calculus. The focus is on uses of partial differential equations: their appearance in pricing financial derivatives, connection with Markov processes, and occurrence as Hamilton-Jacobi-Bellman equations in stochastic control problems, and analytical, asymptotic, and numerical techniques for their solution.

ORF 542 Controlled Markov Processes

Savaş Dayanik

Deterministic optimal control, dynamic programming, and Pontryagin maximum principle. Controlled diffusion processes and stochastic dynamic programming. Hamilton-Jacobi-Bellman equation, viscosity solutions. Merton problem, singular optimal control, option pricing via utility maximization.

ORF 547 Dynamic Programming

Warren B. Powell

Introduction to Markov decision processes and the use of approximate dynamic programming for solving complex sequential decision problems. Problem areas include asset acquisition, high-dimensional shortest-path problems, real- and financial-asset allocation problems, and related pricing problems. Emphasis is on the development of Monte-Carlo–based approximation strategies using stochastic gradient algorithms, forward- and backward-pass updating, pre- and post-decision state variables, Q-learning and temporal difference methods, and recursive regression.

ORF 548 Large-Scale Optimization

John M. Mulvey

Survey of methods for solving large-scale optimization problems, with an emphasis on implementation issues. Topics are chosen from among the following: linear programming-basis partitioning methods, Dantzig-Wolfe decomposition, Benders’ decomposition, and interior point methods; nonlinear programming-conjugate gradient algorithms, quasi-Newton methods, sparse Newton methods, reduced gradient techniques, and trust-region strategies; and parallel optimization-distributed algorithms and single-machine algorithms.

ORF 549 Stochastic Programming

John M. Mulvey

An introduction to the field of stochastic programming. Integrates forecasting and planning systems. Topics include multiobjective optimization, with reference to risks and rewards over time, fundamentals of decision analysis, and stochastic planning systems. Prerequisites include a course in linear programming and multivariate statistics.

ORF 551 Probability Theory (also APC 551)

Erhan Çinlar

Introduction to probability theory, beginning with a review of measure and integration; various concepts of convergence, laws of large numbers, and central limits; martingale theory, filtrations, and stopping times; and Brownian motion, Lévy processes, and Poisson random measures.

ORF 553 Stochastic Differential Equations

René A. Carmona, Erhan Çinlar

The general theory of martingales and semimartingales; stochastic integrals and stochastic differential equations; diffusion processes; Brownian flows, mass transport by flows.

ORF 554 Markov Processes

Erhan Çinlar

Markov processes, with general state spaces; transition semigroups, generators, resolvants; hitting times, jumps, and Lévy systems; additive functionals and random time changes; killing and creation of Markovian motions.

ORF 555 Fixed-Income Models (also FIN 555)

Victoria Henderson

An introduction to continuous-time models for the arbitrage-free pricing of interest-rate derivatives. Topics include primitives of the bond market and the relation between their dynamics, short-rate models, the Heath-Jarrow-Morton methodology and related consistency problems, LIBOR market models, affine term-structure models, and risk of default.

ORF 557, 558 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 562 Transportation and Logistics Planning

Warren B. Powell

Operations research in transportation, logistics, and operations planning; static, dynamic, and stochastic inventory models; multilocational inventory methods and their extension to dynamic fleet management; dynamic routing over transportation networks; equilibrium models for traffic assignment; and the vehicle routing problem. The focus of the course is the modeling process, and the formulation and solution of mathematical problems that arise in an operational context. Additional techniques are introduced as needed. The course is open to advanced undergraduates. Prerequisities: optimization and stochastic models.

ORF 563 Transportation

Alain L. Kornhauser

Interactions between urban transportation and urban development in a comparative study of spatial urban patterns and their corresponding transportation systems. Discussion of basic urban travel characteristics, with the analytical tools used in evaluating movement systems, the implication of transportation networks for urban development policies, and the interrelationship of different modes of transportation.

ORF 569, 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 572 Risk Management Seminar

Staff

Advanced topics in the theory and application of financial risk analysis and modeling. Exact content varies from year to year, covering measures of risk, risk of default, credit derivatives, real options, dynamic asset allocation, and estimation of random processes.

ORF 574 Special Topics in Investment Science

John M. Mulvey

The emphasis is 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 relationships between macro-economic variables and various hedge-fund trading strategies; analyze hedge funds from the standpoint of asset allocation and efficient frontier models. We 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

K. Ronnie Sircar

Topics include stochastic volatility modeling for financial derivatives problems, stochastic optimization problems in finance, and risk management problems in insurance.

Undergraduate Courses of Interest

The following courses listed in the Undergraduate Announcement are open for election by graduate students who have not had their equivalent before coming to graduate school.

Mathematics

308 Theory of Games

314 Introduction to Real Analysis