Operations Research and Financial Engineering

Academic Year: 
2021-22
Department or Program: 
Operations Research and Financial Engineering
Address: 
Sherrerd Hall
Website: 
Department of Operations Research and Financial Engineering
Program offerings: 
Ph.D.
M.S.E.
M.Eng.
Director of Graduate Studies
Mykhaylo Shkolnikov
Graduate Program Administrator
Kimberly Lupinacci

Overview

Foundations
The Operations Research and Financial Engineering (ORFE) program places a strong emphasis on mathematical and computational tools. Students in ORFE develop a unique set of skills that build upon a solid foundation in probability, statistics, and optimization.

Applications
The theoretical foundations of ORFE are of central importance in many complex problems in engineering and science. Students and faculty in ORFE work in a broad range of application areas, such as finance, energy, health, risk analysis, biostatistics, genomics, machine learning, operations research, stochastic networks, signal and image processing, automated vehicle control systems, optimal design of engineered systems, robotics, astrophysics, and homeland security.

Impact
Graduates of the Ph.D. program work in academia, research organizations, and industry. Many ORFE graduates hold faculty positions at top universities.

The department ordinarily 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 also a major participant in the Master of Finance (M.Fin.) program offered through the Bendheim Center for Finance.

Applying

Application Deadline: 
January 3, 11:59 p.m. Eastern Standard Time
Program Length: 
Ph.D. 4 years, M.S.E. 2 years
Application Fee: 
$75
Application Requirements: 
Statement of Academic Purpose
Resume/Curriculum Vitae
Recommendation Letters
Transcripts
Fall Semester Grades
Required Tests
English Language Tests
GRE : 
General Test optional/not required; Subject Test in Mathematics strongly rcommended.
Additional Departmental Requirements: 
  • M.S.E. applicants are required to have the endorsement of a faculty member who is willing to supervise them prior to submitting an application.
  • M.S.E. applicants are required to submit a Statement of Financial Resources.

Ph.D.

Ph.D. Requirements: 
Courses:

In consultation with the director of graduate studies, students develop a specific course plan. During the first year, students complete six courses that emphasize the foundations of the program, probability, statistics, and optimization. Students take at least ten courses while enrolled: the six core courses during the first year, two directed research courses, and two additional advanced-level courses in the second year. 

The following six core courses are required:

  • ORF 522 Linear and Nonlinear Optimization
  • ORF 523 Convex and Conic Optimization
  • ORF 524 Statistical Theory and Methods
  • ORF 525 Statistical Foundations of Data Science
  • ORF 526 Probability Theory
  • ORF 527 Stochastic Calculus

In addition, at least two advanced courses and two semesters of directed research (ORF 509 and ORF 510) are completed under the direction of a faculty adviser in the student's area of interest by the end of the second year in preparation for the general examination.

Pre-Generals Requirement(s):

Research Adviser
Students ordinarily match with an adviser by the end of the first year of study to begin research in preparation for the general examination. No student may enter the second year without a research adviser of record. Students are expected to identify a faculty adviser in the ORFE department. If a student receives permission to work with a faculty adviser who is not a member of the ORFE department, the student must also have a co-adviser who is on the ORFE faculty and is seriously involved in co-advising the student.

Qualifying Examination
Each student must satisfy qualifying requirements. Qualifying exams are offered in September of the student’s second year. 

A student who obtained a grade of A- or better in four of the six required core classes will be exempt from the September qualifying exams. If this is not the case, the student will meet with the DGS to determine which exams need to be taken in September to satisfy the requirements. 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. 

A vote of the faculty determines the results of the qualifying exam. Students who fail must transfer out of the Ph.D. program. There is no option to retake the exam.  The examination is roughly 90 minutes/course.  Students will be provided the questions a few hours before the examination.  Two faculty examiners will evaluate the student’s performance on the examination.  Additional information related to the preliminary examination is outlined in the graduate student handbook.

General Exam:

ORFE students take the general exam in April or May of their second year.  To be eligible to stand for the general examination, students must have completed the required core courses, met the qualifying examination requirements, have taken and passed ORF 509, have taken or are currently enrolled in ORF 510, and have received a B+ or higher in two additional advanced courses at the 500 level. The student must also show adequate progress on research and an acceptable level of understanding of their area of specialization.

The general examination consists of two parts, a written and oral component, both covering the student's area of specialty. The written component is completed by submitting a 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 oral component is completed by giving a presentation on the research presented in the comprehensive written report. The oral exam may be up to 3 hours in length.

As part of the oral examination, the general examination committee may ask questions related to the research and the student’s area of specialization.   

For each student, an examining committee is selected by the student and adviser. In addition to the adviser, the committee consists of two ORFE faculty or affiliated faculty and must be approved by the Director of Graduate Studies. The committee will administer the oral exam, evaluate the student’s performance in research and overall knowledge of the student's field, and make a recommendation to the department faculty. A departmental faculty vote determines the final outcome.

Qualifying for the M.A.:

The Master of Arts (M.A.) degree is normally an incidental degree on the way to full Ph.D. candidacy and is earned after a student successfully passes the general examination. It may also be awarded to students who, for various reasons, leave the Ph.D. program, provided that these requirements have been met.

Please note, students admitted to the Ph.D. program who do not wish to complete the program may be considered for an M.S.E. degree with approval from the department and the Graduate School. Ph.D. students who have already been awarded the incidental M.A. are not eligible to earn an M.S.E. 

Dissertation and FPO:

Upon completion and acceptance of the dissertation by the department, the candidate will be admitted to the final public oral (FPO) examination.

The committee of examiners for the FPO must consist of no fewer than two current ORFE faculty members, and the 2nd thesis reader should also be a current ORFE faculty member.

The Ph.D. is awarded after the candidate’s doctoral dissertation has been accepted and the final public oral examination sustained.

M.S.E.

M.S.E. Requirements: 
Program Description:

The ORFE department is primarily geared towards educating students pursuing a Ph.D. in the field. As such, the Master of Science in Engineering (M.S.E.) program in ORFE also has a strong research focus, as reflected in the requirement of a thesis and full-time study for two academic years. Students enrolled in this program are eligible for financial support in the form of research or teaching assistantships if such funds are available.

The admission rate for the M.S.E. degree is very low. Admission is based on the applicant's qualifications and requires the support of at least one faculty member who expresses an interest in supervising the applicant. Applicants interested in an M.S.E. degree from ORFE are urged to identify and contact a faculty member who researches in an area the applicant would like to work.

Applicants primarily interested in a master's degree in finance should apply for the Master in Finance Program at the Bendheim Center for Finance. The School of Engineering website provides more information regarding the Master of Science in Engineering program.

Courses:

The course requirements are fulfilled by successfully completing ten one-semester courses approved by the department, two of which are required research courses (ORF 509 and 510).

Thesis:

The M.S.E. program has a strong research focus reflected in the requirement of a thesis. Upon completion and acceptance of the thesis by the department, the candidate will be admitted to the final defense, administered by at least two faculty members.

M.Eng.

M.Eng. Requirements: 
Program Description:

The Master of Engineering (M.Eng.) is a coursework-based master's degree offered, in 2021-22, to current ORFE Seniors. Candidates for the M.Eng. degree will be enrolled full-time throughout the 10-month academic year. No research or thesis is required. Any class (or its graduate equivalent) counted towards the Princeton undergraduate degree cannot be counted for the M.Eng. degree.

Courses:

Candidates for the M.Eng. degree must successfully complete at least eight approved courses. A minimum of six of these eight courses must be technical, having their primary listing in a department or a program within the natural sciences or engineering. A minimum of four of these six courses must be chosen from graduate offerings in the Department of Operations Research & Financial Engineering; options include any of the following six core courses for the Ph.D. degree.  Students must have a “B” (3.0) average or better when they complete the program requirements to receive the degree.


ORF 522- Linear & Nonlinear Optimization
ORF 523- Convex and Conic Optimization
ORF 524- Statistical Theory and Methods
ORF 525- Statistical Foundations of Data Science
ORF 526- Probability Theory
ORF 527- Stochastic Calculus


As well as several graduate-level ORFE electives
ORF 504- Financial Econometrics
ORF 505- Statistical Analysis of Financial Data
ORF 515- Asset Pricing II: Stochastic Calculus and Advanced Derivatives
ORF 531- Computational Finance in C++
ORF 535- Financial Risk Management
ORF 538- PDE Methods in Financial Mathematics
ORF 542- Stochastic Control and Stochastic Differential Games
ORF 545- High-Frequency Markets
ORF 569- Special Topics in Statistics, Operations Research and Financial Engineering
ORF 570- Special Topics in Statistics, Operations Research and Financial Engineering


Other approved classes include:
ORF 401- Electronic Commerce
ORF 407- Fundamentals of Queueing Theory
ORF 409- Introduction to Monte Carlo Simulation
ORF 418- Sequential Decision Analytics and Modeling
ORF 435- Financial Risk and Wealth Management
ORF 455- Energy & Commodities Markets
ORF 473- Special Topics in Operations Research and Financial Engineering
ORF 474- Special Topics in Operations Research and Financial Engineering
Courses of potential interest in other departments:
APC 503- Analytical Techniques in Differential Equations
COS 402- Machine Learning and Artificial Intelligence
COS 423- Theory of Algorithms
COS 485- Neural Networks: Theory and Application
COS 511- Theoretical Machine Learning
COS 521- Advanced Algorithm Design
COS 528- Data Structures and Graph Algorithms
COS 534- Fairness in Machine Learning
ECO 418- Strategy and Information
ECO 462- Portfolio Theory and Asset Management
ECO 464- Corporate Restructuring
ECO 466- Fixed Income: Models and Applications
ECO 467- Institutional Finance
ECO 517- Econometric Theory I
ECO 518- Econometric Theory II
ECO 525- Financial Economics I
ECO 526- Financial Economics II
ELE 525- Random Processes in Information Systems
ELE 535- Machine Learning and Pattern Recognition
ELE 538B- Information Sciences and Systems Large Scale Optimization for Data Science
MAE 546- Optimal Control and Estimation
MAT 522/APC 522- Introduction to PDE
MAT 527- Topics in Differential Equations: Global Solutions of Nonlinear Evolutions
MAT 572/APC 572- Introduction to Combinatorial Optimization
MAT 587- Topics in Ergodic Theory: Introduction to Ergodic Theory
MAT 589- Topics in Probability, Statistics, and Dynamics: Modern Discrete Probability Theory
PHY 521/MAT 597- Introduction to Mathematical Physics
SPI 509- Generalized Linear Statistical Models

Faculty

Chair

  • Ronnie Sircar

Director of Graduate Studies

  • Mykhaylo Shkolnikov

Director of Undergraduate Studies

  • Alain L. Kornhauser

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
  • Miklos Z. Racz
  • Elizaveta Rebrova
  • Bartolomeo Stellato
  • Ludovic Tangpi

Associated Faculty

  • Yacine Aït-Sahalia, Economics
  • Markus K. Brunnermeier, Economics
  • Maria Chudnovsky, Mathematics
  • Sanjeev R. Kulkarni, Dean of the Faculty
  • H. Vincent Poor, Electrical & Comp Engineering
  • Paul Seymour, Mathematics
  • John D. Storey, Integrative Genomics

Lecturer

  • Quentin Cormier
  • Miguel Angel Garrido
  • Margaret Holen

Visiting Lecturer

  • Robert Almgren
  • Michael Sotiropoulos
For a full list of faculty members and fellows please visit the department or program website.

Courses

Permanent Courses

Courses listed below are graduate-level courses that have been approved by the program’s faculty as well as the Curriculum Subcommittee of the Faculty Committee on the Graduate School as permanent course offerings. Permanent courses may be offered by the department or program on an ongoing basis, depending on curricular needs, scheduling requirements, and student interest. Not listed below are undergraduate courses and one-time-only graduate courses, which may be found for a specific term through the Registrar’s website. Also not listed are graduate-level independent reading and research courses, which may be approved by the Graduate School for individual students.

FIN 501 Asset Pricing I: Pricing Models and Derivatives (also
ORF 514
) Provides an introduction of the modern theory of asset pricing. Topics include: (i) no arbitrage, Arrow-Debreu prices and equivalent martingale measure; (ii) security structure and market completeness; (iii) mean-variance analysis, Beta-Pricing, CAPM; and (iv) introduction to derivative pricing.
ORF 504 Financial Econometrics (also
FIN 504
) This course covers econometric and statistical methods as applied to finance. Topics include: (i) Measurement issues in finance (ii) Predictability of asset returns and volatilities (iii) Value at Risk and extremal events (iv) Linear factor pricing and portfolio problems (v) Intertemporal models of the Stochastic Discount Factor and Generalized Method of Moments (vi) Vector Autoregressive and maximum likelihood methods in finance (vii) Risk Neutral valuation in discrete time (viii) Estimation methods for continuous time models (ix) Volatility smiles and alternatives to Black-Scholes (x) Nonparametric statistical methods for option pricing.
ORF 505 Statistical Analysis of Financial Data (also
FIN 505
) Linear and mixed effect models. 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 509 Directed Research I 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 one semester prior to taking the general examination.
ORF 510 Directed Research II 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 one semester prior to taking the general examination.
ORF 511 Extramural Summer Project 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 Asset Pricing II: Stochastic Calculus and Advanced Derivatives (also
FIN 503
) Course begins with an overview of basic probability theory and covers the elements of stochastic calculus and stochastic differential equations that are widely used in modern financial applications. Topics include the Poisson process, Brownian motion, martingales, diffusions and their connection with partial differential equations. Examples from applications include the Black-Scholes option pricing and hedging theory, bond pricing and stochastic volatility models.
ORF 522 Linear and Nonlinear Optimization Theoretical concepts underlying linear programming, with computer implementations of some of the different methods. The topics covered include duality theory, the simplex method, interior point methods, related numerical issues, and modeling paradigms.
ORF 523 Convex and Conic Optimization 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: linear optimization.
ORF 524 Statistical Theory and Methods A graduate level introduction to statistical theory and methods. It 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, and hypothesis testing, and the applications of the fundamental theory to linear models and categorical data.
ORF 525 Statistical Foundations of Data Science An introduction to the most important and broadly utilized statistical methods used in many scienti¿c data analysis, including general linear, mixed-e¿ects, generalized linear models, regression and ANOVA models. The methodological power of statistics will be emphasized. Objectives of this course are to give students a solid understanding of these methods, and o¿er them experience in applying these methods to real data using statistical computing packages and interpreting results. For master's/Ph.D. students and advanced undergraduates.
ORF 526 Probability Theory 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, martin- gales, Markov chains, and Poisson processes.
ORF 527 Stochastic Calculus 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 531 Computational Finance in C++ (also
FIN 531
) 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 535 Financial Risk and Wealth Management (also
FIN 535
) 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. Lectures meet concurrently with ORF 435. Credit for graduate course requires completion of additional assignments.
ORF 538 PDE Methods for Financial Mathematics 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 Optimal Control 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 543 Deep Learning Theory This course is an introduction to deep learning theory. Using tools from mathematics (e.g. probability, functional analysis, spectral asymptotics and combinatorics) as well as physics (e.g. effective field theory, the 1/n expansion, and the renormalization group) we cover topics in approximation theory, optimization, and generalization.
ORF 544 Stochastic Optimization This course provides a unified presentation of stochastic optimization, cutting across classical fields including dynamic programming (including Markov decision processes), stochastic programming, (discrete time) stochastic control, model predictive control, stochastic search, and robust/risk averse optimization, as well as related fields such as reinforcement learning and approximate dynamic programming. Also covered are both offline and online learning problems. Considerable emphasis is placed on modeling and computation.
ORF 545 High Frequency Markets: Models and Data Analysis (also
FIN 545
) An introduction to the microstructure of modern electronic financial markets and high frequency trading strategies. Topics include market structure and optimization techniques used by various market participants, tools for analyzing limit order books at high frequency, and stochastic dynamic optimization strategies for trading with minimal market impact at high and medium frequency. The course makes essential use of high-frequency futures data, accessed using the Kdb+ database language. Graduate credit requires completion of extended and more sophisticated homework assignments.
ORF 550 Topics in Probability (also
APC 550
) An introduction to nonasymptotic methods for the study of random structures in high dimension that arise in probability, statistics, computer science, and mathematics. Emphasis is on developing a common set of tools that has proved to be useful in different areas. Topics may include: concentration of measure; functional, transportation cost, martingale inequalities; isoperimetry; Markov semigroups, mixing times, random fields; hypercontractivity; thresholds and influences; Stein's method; suprema of random processes; Gaussian and Rademacher inequalities; generic chaining; entropy and combinatorial dimensions; selected applications.
ORF 569 Special Topics in Statistics, Operations Research and Financial Engineering Advanced topics in statistics and operations research or the investigation of problems of current interest.
ORF 570 Special Topics in Statistics and Operations Research (also
ECE 578
) Advanced topics in statistics and operations research or the investigation of problems of current interest.
ORF 574 Special Topics in Investment Science (also
FIN 574
) 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.