Operations Research and Financial Engineering

Academic Year: 
2016-17
Address: 
Sherrerd Hall
Website: 
Department of Operations Research and Financial Engineering
Program offerings: 
Ph.D.
M.S.E.
Director of Graduate Studies
Warren Powell
Graduate Program Administrator
Kimberly Lupinacci

Academic department detail

Overview
Foundations

The ORFE program places a strong emphasis on quantitative methods and mathematical modeling. 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, and homeland security.

Impact

ORFE faculty is renowned within the field. They have won numerous awards for their research and are fellows of the major scientific societies in their research areas. Graduates of the Ph.D. program work in academia, research organizations, and industry. Many of them have taken positions at top universities.

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.

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 and introduction ot the mofern theory of asset pricing. Topics include: (1) 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 Learning and Nonparametric Estimation 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 534 Quantitative Investment Management (also
FIN 534
) 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
) 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 Control and Stochastic Differential Games 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 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 548 Large-scale Optimization Survey of methods for solving large-scale optimization problems, with an emphasis on implementation issues. Topics are chosen from 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 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 553 Stochastic Differential Equations 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 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 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 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 Operations research in transportation, logistics, and operations planning; static, dynamic, and stochastic inventory models; multilocational inventory methods and their extention 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. Prerequisites: optimization and stochastic models.
ORF 566 High Dimensional Statistics Course is on statistical theory and methods for high-dimensional statistical learning and inferences arising from processing massive data from various scientific disciplines. Emphasis is given to penalized likelihood methods, independence screening, large covariance modeling, and large-scale hypothesis testing. The important theoretical results are proved.
ORF 569 Special Topics in Statistics and Operations Research Advanced topics in statistics and operations research or the investigation of problems of current interest.
ORF 570 Special Topics in Statistics and Operations Research 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.
ORF 575 Financial Engineering Seminar Topics include stochastic volatility modeling for financial derivatives problems, stochastic optimization problems in finance and risk management problems in insurance.