Oper Res and Financial Engr

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. Applicability and limitations of these methods will be illustrated in the light of modern data sets and manipulation of the statistical software R. Precepts are based on real data analysis.

ORF 307/EGR 307: OptimizationMany realworld problems involve maximizing a linear function subject to linear equality and/or inequality constraints. Such problems are called Linear Programming (LP) problems. Examples include mincost network flows, portfolio optimization, options pricing, assignment problems and twoperson zerosum games to name but a few. The theory of linear programming will be developed with a special emphasis on duality theory. Attention will be devoted to efficient solution algorithms. These algorithms will be illustrated on realworld examples such as those mentioned.

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 311: Stochastic Optimization and Machine Learning in FinanceA survey of quantitative approaches for making optimal decisions under uncertainty, including decision trees, Monte Carlo simulation, and stochastic programs. Forecasting and planning systems are integrated in the context of financial applications. Machine learning methods are linked to the stochastic optimization models.

ORF 335/ECO 364: Introduction to Financial MathematicsFinancial Mathematics is concerned with designing and analyzing products that improve the efficiency of markets, and create mechanisms for reducing risk. This course develops quantitative methods for these goals: the notions of arbitrage and riskneutral pricing in discrete time, specific models such as BlackScholes and Heston in continuous time, and calibration to market data. Credit derivatives, the term structure of interest rates, and robust techniques in the context of volatility options will be discussed, as well as lessons from the financial crisis.

ORF 350: Analysis of Big DataThe amount of data in our world has been exploding and analyzing large data sets is a central challenge in society. This course introduces the statistical principles and computational tools for analyzing big data. Topics include statistical modeling and inference, model selection and regularization, scalable computational algorithms, and more.

ORF 376: Independent Research ProjectIndependent research or investigation resulting in a report in the student's area of interest under the supervision of a faculty member. Open to sophomores and juniors.

ORF 387: NetworksThis course showcases how networks are widespread in society, technology, and nature, via a mix of theory and applications. It demonstrates the importance of understanding network effects when making decisions in an increasingly connected world. Topics include an introduction to graph theory, game theory, social networks, information networks, strategic interactions on networks, network models, network dynamics, information diffusion, and more.

ORF 401: Electronic CommerceElectronic commerce, traditionally the buying and selling of goods using electronic technologies, extends to essentially all facets of human interaction when extended to services, particularly information. The course focuses on both the software and the hardware aspects of traditional aspects as well as the broader aspects of the creation, dissemination and human consumption electronic services. Covered will be the physical, financial and social aspects of these technologies

ORF 407: Fundamentals of Queueing TheoryThis is an introduction to the stochastic models inspired by the dynamics of resource sharing. Topics discussed include: early motivating communication systems (telephone and computer networks); modern applications (call centers, healthcare operations, and urban planning for smart cities); and key formulas (from Erlang blocking and delay to Little's law). We also review supporting stochastic theories like equilibrium Markov chains along with Markov, Poisson and renewal processes.

ORF 473: Special Topics in Operations Research and Financial Engineering: Financial Technology and DataDriven InnovationIn recent years, financial services have significantly evolved through datadriven innovation. This course will review the landscape broadly and then focus on case studies in automated lending enabled by machine learning. Students will study specific machine learning methods in current use and will be introduced to issues of fairness and explainability, which are increasingly important in this sector and beyond. Overall, the class will integrate mathematical finance models, machine learning methods and practical industry perspectives.

ORF 474: Special Topics in Operations Research and Financial Engineering: High Frequency Markets: Models and Data AnalysisAn introduction to the theory and practice of high frequency trading in modern electronic financial markets. We give an overview of the institutional landscape and basic empirical features of modern equity, futures, and fixed income markets. We discuss theoretical models for market making and price formation. Then we dig into detailed empirical aspects of market microstructure and how these can be used to constructe effective trading strategies. Course work will be a mixture of theoretical and datadriven problems. Programming environment will be a mixture of the R statistical environment, with the Kdb database language.

ORF 478: 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, and the thesis is defended by the student at a public examination before a faculty committee. The senior thesis is equivalent to a yearlong study and is recorded as a double course in the Spring.

ORF 479: Senior ProjectStudents conduct a onesemester project. Topics chosen by students with approval of the faculty. A written report is required at the end of the term.

ORF 504/FIN 504: Financial EconometricsEconometric and statistical methods as applied to finance. Topics include: Asset returns and efficient markets, linear time series and dynamics of returns, volatility models, multivariate time series, efficient portolios and CAPM, multifactor pricing models, portfolio allocation and risk assessment, intertemporal equilibrium models, present value models, simulation methods for financial derivatives, econometrics of continuous time finance.

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 515/FIN 503: Asset Pricing II: Stochastic Calculus and Advanced DerivativesThe course covers the pricing and hedging of advanced derivatives, including topics such as exotic options, greeks, interest rate and credit derivatives, as well as risk management. The course further covers basics of stochastic calculus necessary for finance. Designed for Masters students.

ORF 523: Convex and Conic OptimizationA mathematical introduction to convex, conic, and nonlinear optimization. Topics include convex analysis, duality, theorems of alternatives and infeasibility certificates, semidefinite programming, polynomial optimization, sum of squares relaxation, robust optimization, computational complexity in numerical optimization, and convex relaxations in combinatorial optimization. Applications drawn from operations research, dynamical systems, statistics, and economics.

ORF 525: Statistical Foundations of Data ScienceA theoretical introduction to statistical machine learning for data science. It covers multiple regression, kernel learning, sparse regression, high dimensional statistics, sure independent screening, generalized linear models, covariance learning, factor models, principal component analysis, supervised and unsupervised learning, deep learning, and related topics such as community detection, item ranking, and matrix completion.These methods are illustrated using real world data sets and manipulation of the statistical software R.

ORF 527: Stochastic CalculusAn 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; FeynmanKac formula.

ORF 569: Special Topics in Operations Research and Financial Engineering: Probabilistic Theory of Network Games and Mean Field InteractionsThe seminar course presents recent developments in the theory of large stochastic systems. The first part of the course is focused on the equilibrium theory of game models when the interactions between the agents is through a large network modeled with a weighted random graph. The second part of the course focuses on probabilistic models with singular mean field interactions and applications to free boundary problems in material science, financial networks and neuroscience.