Graduate Courses

Asset Pricing I: Pricing Models and Derivatives
Subject associations
FIN 501 / ORF 514

An 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.

Instructors
Moritz F. Lenel
Fall 2021
Asset Pricing I: Pricing Models and Derivatives
Subject associations
FIN 501 / ORF 514

An 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.

Instructors
Moritz F. Lenel
Fall 2022
Asset Pricing II: Stochastic Calculus and Advanced Derivatives
Subject associations
ORF 515 / FIN 503

The 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.

Instructors
Spring 2022
Computational Finance in C++
Subject associations
ORF 531 / FIN 531

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.

Instructors
Michael Sotiropoulos
Fall 2021
Computational Finance in C++
Subject associations
ORF 531 / FIN 531

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.

Instructors
Michael Sotiropoulos
Fall 2022
Convex and Conic Optimization
Subject associations
ORF 523

A 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.

Instructors
Spring 2022
Deep Learning Theory
Subject associations
ORF 543

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.

Instructors
Fall 2021
Deep Learning Theory
Subject associations
ORF 543

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.

Instructors
Fall 2022
Directed Research I
Subject associations
ORF 509

Under 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.

Instructors
Fall 2021
Directed Research I
Subject associations
ORF 509

Under 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.

Instructors
Fall 2022
Directed Research II
Subject associations
ORF 510

Under 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.

Instructors
Spring 2022
Extramural Summer Project
Subject associations
ORF 511

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.

Instructors
Summer 2021
Extramural Summer Project
Subject associations
ORF 511

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.

Instructors
Summer 2022
Financial Econometrics
Subject associations
ORF 504 / FIN 504

Econometric 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.

Spring 2022
Financial Risk and Wealth Management
Subject associations
ORF 535 / FIN 535

This 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.

Instructors
Fall 2021
Financial Risk and Wealth Management
Subject associations
ORF 535 / FIN 535

This 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.

Instructors
Fall 2022
High Frequency Markets: Models and Data Analysis
Subject associations
ORF 545 / 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.

Instructors
Robert Almgren
Spring 2022
Linear and Nonlinear Optimization
Subject associations
ORF 522

This 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.

Instructors
Fall 2021
Linear and Nonlinear Optimization
Subject associations
ORF 522

This 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.

Instructors
Fall 2022
Probability Theory
Subject associations
ORF 526

This 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.

Instructors
Fall 2021
Probability Theory
Subject associations
ORF 526

This 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.

Instructors
Fall 2022
Special Topics in Statistics, Operations Research and Financial Engineering: Theory and Practice of Deep Learning
Subject associations
ORF 569

This introductory course on the theory of deep learning, emphasizes the integrated nature of theory, exploratory empirical work, and concrete solutions to difficult machine learning problems.

Instructors
Fall 2022
Statistical Analysis of Financial Data
Subject associations
ORF 505 / FIN 505

The 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.

Instructors
Fall 2021
Statistical Analysis of Financial Data
Subject associations
ORF 505 / FIN 505

The 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.

Instructors
Fall 2022
Statistical Foundations of Data Science
Subject associations
ORF 525

A 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.

Instructors
Spring 2022
Statistical Theory and Methods
Subject associations
ORF 524

A graduate-level introduction to statistical theory and methods and some of the most important and commonly-used principles of statistical inference. Covers the statistical theory and methods for point estimation, confidence intervals (including modern bootstrapping), and hypothesis testing. These topics will be covered in both nonparametric and parametric settings, and from asymptotic and non-asymtoptotic viewpoints. Basic ideas from measure-concentration and notions of capacity of functional classes (e.g. VC, covering and bracketting numbers) will be covered as needed to support the theory.

Instructors
Fall 2021
Statistical Theory and Methods
Subject associations
ORF 524

A graduate-level introduction to statistical theory and methods and some of the most important and commonly-used principles of statistical inference. Covers the statistical theory and methods for point estimation, confidence intervals (including modern bootstrapping), and hypothesis testing. These topics will be covered in both nonparametric and parametric settings, and from asymptotic and non-asymtoptotic viewpoints. Basic ideas from measure-concentration and notions of capacity of functional classes (e.g. VC, covering and bracketting numbers) will be covered as needed to support the theory.

Instructors
Fall 2022
Stochastic Calculus
Subject associations
ORF 527

An 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; Feynman-Kac formula.

Instructors
Spring 2022
Stochastic Optimal Control
Subject associations
ORF 542

We start this lecture by introducing some classical stochastic control problems, including optimal portfolio allocation, Merton utility maximization problem, real option, and contract theory. This introduction motivates us to study, after a short recall on stochastic calculus, some ways to solve stochastic control problems as well as optimal stopping problem. This leads us on a journey through the dynamic programming principle, the Hamilton Jacobi Bellman (HJB) equations, the notion of viscosity solution, up to the theory of BSDEs.

Instructors
Spring 2022
Stochastic Optimization
Subject associations
ORF 544

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.

Instructors
Warren B. Powell
Fall 2021
Topics in Probability: Probability in High Dimension
Subject associations
ORF 550 / 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.

Instructors
Fall 2021