Operations Research and Financial Engineering

An individual makes decisions every day. In addition, other people are making decisions that have an impact on the individual. In this course we will consider both how these decisions are made and how they should be made. In particular, we will focus on the use of advanced computing and information technology in the decision-making process.

A 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. Prerequisite MAT 201 equivalent or concurrent. Two 90 minute lectures, one preceptorial.

Many real-world problems involve maximizing a linear function subject to linear inequality constraints. Such problems are called Linear Programming (LP) problems. Examples include min-cost network flows, portfolio optimization, options pricing, assignment problems and two-person zero-sum 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 real-world examples such as those mentioned. Two 90 minute lectures, one preceptorial. Prerequisite MAT 202 or 204.

An 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. Three lectures, one precept. Prerequisite: MAT 201 or instructor's permission.

A 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.. Prerequisites: ORF 307 or MAT 305, and 309. Two 90-minute classes, one preceptorial.

A multidisciplinary study of the fundamentals of human-machine interactions from both the human psychology/philosophy side and the machine engineering and design side. Philosophical, psychological, and engineering models of the human processor. Functional differences between people and machines, the nature of consciousness and intelligence, massively parallel computing and neural networks, and the concept of resonant synergism in human-machine interactions. Two 90-minute lectures; three laboratories during semester.

This course introduces the basics of quantitative finance, particularly the use of stochastic models to value and hedge risks from options, futures and other derivative securities. The models studied include binomial trees in discrete time, and the Black-Scholes theory is introduced in continuous-time models. Computational methods are introduced in Matlab. The second half of the class looks at modern topics such as credit risk, stochastic volatility, portfolio optimization, as well as lessons from the financial crisis. Prerequisites: ORF 309, ECO 100, and MAT 104.

The 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. Prerequisite: ORF 245, ORF 309. Lecture and precept.

This is an introductory course to decision methods and modeling in business and operations management. The course will emphasize both mathematical decision-making techniques, as well as popular data-based decision models arising from real applications. Upon completion of this course students will have learned analytical tools for modeling and optimizing business decisions. From a practical perspective, this will be a first course that gives an overview of advanced operations research topics including revenue management, supply chain management, network management, and pricing.

An introduction to several fundamental and practically-relevant areas of numerical computing with an emphasis on the role of modern optimization. Topics include computational linear algebra, descent methods, basics of linear and semidefinite programming, optimization for statistical regression and classification, trajectory optimization for dynamical systems, 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, finance, economics, control theory, and engineering. A. Ahmadi,

A course covering special topics in operations research or financial engineering. Subjects may vary from year to year.

Independent research or investigation resulting in a substantial formal report in the student's area of interest under the supervision of a faculty member. Open to sophomores and juniors.

Independent research or investigation resulting in a substantial formal report in the student's area of interest under the supervision of a faculty member. Open to sophomores and juniors.

Electronic 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. Two 90-minute lectures, one 50-minute preceptorial.

Statistical Analysis of financial data: Density estimation, heavy tail distributions and dependence. Regression: linear, nonlinear, nonparametric. Time series analysis: classical models (AR, MA, ARMA), state space systems and filtering, and stochastic volatility models (ARCH, GARCH). Prerequsites: ORF 245 and MAT 202.

Major methods of statistics as applied to the engineering and physical sciences. The central theme is the construction of empirical models, the design of experiments for elucidating models, and the applications of models for forecasting and decision making under uncertainty. Three lectures. Prerequisite: 245 or equivalent.

This 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. Prerequisite: ORF 309 or equivalent.

An 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.Prerequisite: ORF 309.

The management of complex systems through the control of physical, financial and informational resources. The course focuses on developing mathematical models for resource allocation, with an emphasis on capturing the role of information in decisions. The course seeks to integrate skills in statistics, stochastics and optimization using applications drawn from problems in dynamic resource management which tests modeling skills and teamwork. Prerequisites: ORF 245, ORF 307 and ORF 309, or equivalents. Two 90 minute lectures, preceptorial.

An introduction to stochastic dynamic programming and stochastic control. The course deals with discrete and continuous-state dynamic programs, finite and infinite horizons, stationary and nonstationary data. Applications drawn from inventory management, sequential games, stochastic shortest path, dynamic resource allocation problems. Solution algorithms include classical policy and value iteration for smaller problems and stochastic approximation methods for large-scale applications. Prerequisites: 307 and 309.

Addresses the problem of collecting information used to estimate statistics or fit a model which is then used to make decisions. Of particular interest are sequential problems where decisions adapt to information as it is learned. The course introduces students to a wide range of applications, demonstrates how to express the problem formally, and describes a variety of practical solution strategies. Prerequisite: ORF 245, ORF 309. Two 90-minute lectures, one preceptorial.

This course covers the basic concepts of modeling, measuring and managing different types of financial risks. Topics include portfolio optimization (mean-variance approach and expected utility), interest rate risk, pricing and hedging in complete and incomplete markets, indifference pricing, risk measures, systemic risk. Prerequisites: ORF 245, ORF 335 or ECO 465 (concurrent enrollment is acceptable) or instructor's permission. Two 90-minute lectures, one preceptorial.

This course is an introduction to commodities markets (energy, metals, agricultural products) and issues related to renewable energy sources such as solar and wind power, and carbon emissions. Energy and other commodities represent an increasingly important asset class, in addition to significantly impacting the economy and policy decisions. Emphasis will be on the term structure of commodity prices: behavior, models and empirical issues. Prerequisite: ORF 335 or instructor permission. Two 90 minute lectures, one precept.

Studied 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 dynamic "value pricing", real-time fleet management and control, GPS-based route guidance systems, automated transit networks and the emergence of Smart Driving / Autonomous Cars. Two 90-minute lectures, one preceptorial.

A course covering one or more advanced topics in operations research and financial engineering. Subjects may vary from year to year.