## Oper Res and Financial Engr

- FIN 501/ORF 514: Asset Pricing I: Pricing Models and DerivativesAn introduction to the modern theory of asset pricing. Topics include: No arbitrage, Arrow-Debreu prices and equivalent martingale measure; security structure and market completeness; mean-variance analysis, Beta-Pricing, CAPM; and introduction to derivative pricing.
- ORF 245/EGR 245: Fundamentals of StatisticsA 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.
- ORF 309/EGR 309/MAT 380: Probability and Stochastic SystemsAn 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
- ORF 363/COS 323: Computing and Optimization for the Physical and Social SciencesAn introduction to several fundamental and practically-relevant areas of modern optimization and numerical computing. Topics include computational linear algebra, first and second order descent methods, convex sets and functions, basics of linear and semidefinite programming, optimization for statistical regression and classification, 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 and machine learning, economics, control theory, and engineering.
- ORF 375: Independent Research ProjectIndependent research or investigation resulting in a substantial formal report in the student's area of interest under the supervision of a faculty member.
- ORF 405: Regression and Applied Time SeriesAn introduction to popular statistical approaches in regression and time series analysis. Topics will include theoretical aspects and practical considerations of linear, nonlinear, and nonparametric modeling (kernels, neural networks, and decision trees).
- ORF 409: Introduction to Monte Carlo SimulationAn 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.
- ORF 418: Optimal LearningThis course develops several methods that are central to modern optimization and learning problems under uncertainty. These include dynamic programming, linear quadratic regulator, Kalman filter, multi-armed bandits and reinforcement learning. Representative applications and numerical methods are emphasized.
- ORF 435: Financial Risk and Wealth ManagementThis course covers the basic concepts of measuring, modeling and managing risks within a financial optimization framework. Topics include single and multi-stage financial planning systems. Implementation from several domains within asset management and goal based investing. Machine learning algorithms are introduced and linked to the stochastic planning models. Python and optimization exercises required.
- ORF 455/ENE 455: Energy and Commodities MarketsThis course is an introduction to commodities markets (oil, gas, metals, electricity, etc.), and quantitative approaches to capturing uncertainties in their demand and supply. We start from a financial perspective, and traditional models of commodity spot prices and forward curves. Then we cover modern topics: game theoretic models of energy production (OPEC vs. fracking vs. renewables); quantifying the risk of intermittency of solar and wind output on the reliability of the electric grid (mitigating the duck curve); financialization of commodity markets; carbon emissions markets. We also discuss economic and policy implications.
- ORF 467: Transportation Systems AnalysisStudied 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 "value" pricing, real-time fleet management and control, GPS-based route guidance systems, automated transit systems and autonomous vehicles will provide a practical focus for the methodologies. Class project in lieu of final exam focused on major issue in Transportation Systems Analysis.
- ORF 498: Senior Independent Research FoundationsThis foundational class is designed to introduce students to both the ideation and investigation components of research, with milestones guiding students towards a complete thesis in the spring semester. Classes will consist of presentations on research tools (including data, library, and computing resources), crash-courses in common research methodologies, and introduction to LaTeX for typesetting their final theses. Throughout the semester, students will discuss and present their thesis progress in smaller group settings. Past student theses will also be studied as examples.
- ORF 499: Senior ThesisA 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. The thesis is submitted and defended by the student at a public examination before a faculty committee. This course completes the research work begun in ORF 498.
- ORF 505/FIN 505: Statistical Analysis of Financial DataThe course is divided into three parts of approximately the same lengths. Density estimation (heavy tail distributions) and dependence (correlation and copulas). Regression analysis (linear and robust alternatives, nonlinear, nonparametric,classification.) Machine learning (TensorFlow, neural networks, convolution networks and deep learning). The statistical analyzes, computations and numerical simulations are done in R or Python.
- ORF 509: Directed Research IUnder the direction of a faculty member, each student carries out research and presents the results. Directed Research is normally taken during the first year of study.
- ORF 510: Directed Research IIUnder the direction of a faculty member, each student carries out research and presents the results. Directed Research II has to be taken before the General Exam.
- ORF 522: Linear and Nonlinear OptimizationThis course introduces analytical and computational tools for linear and nonlinear optimization. Topics include linear optimization modeling, duality, the simplex method, degeneracy, sensitivity analysis and interior point methods. Nonlinear optimality conditions, KKT conditions, first order and Newton's methods for nonlinear optimization, real-time optimization and data-driven algorithms. A broad spectrum of applications in engineering, finance and statistics is presented.
- ORF 524: Statistical Theory and MethodsA graduate-level introduction to statistical theory and methods covering some of the most important and commonly-used principles of mathematical statistics and statistical learning. Covers the statistical theory and methods for point estimation, hypothesis testing, and confidence intervals. These topics are covered in both nonparametric, semiparametric, and parametric settings, and from asymptotic and non-asymtoptotic viewpoints.
- ORF 526: Probability TheoryThis is a graduate introduction to probability theory with a focus on stochastic processes. Topics include: an introduction to mathematical probability theory, law of large numbers, central limit theorem, conditioning, filtrations and stopping times, Markov processes and martingales in discrete and continuous time, Poisson processes, and Brownian motion.
- ORF 531/FIN 531: Computational Finance in C++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 is introduced to C++, the weekly homework involves writing C++ code, and the final project also involves programming in the same environment.
- ORF 535/FIN 535: Financial Risk and Wealth ManagementThis course covers the basic concepts of measuring, modeling and managing risks within a financial optimization framework. Topics include single and multi-stage financial planning systems. Implementation from several domains within asset management and goal based investing. Machine learning algorithms are introduced and linked to the stochastic planning models. Python and optimization exercises required.
- ORF 543: Deep Learning TheoryThis 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.