Financial Mathematics Course Descriptions

Part I (MATH 5075) of this sequence is an introduction to foundational concepts and techniques in applied mathematics and financial economics employed by practitioners and researchers in banking, investments, and financial risk management. In support of arbitrage theory, we will review mathematical probability and discrete-time stochastic processes. In parallel, we will use primary sources to study the properties of traded financial instruments, including securities, indexes, and derivatives. We will combine these streams to create contingent claims models for vanilla derivatives and resolve their value processes using risk-neutral expectation and dynamic replication.

In Part II (MATH 5076), we will transition to the continuous-time setting and cement the theoretical foundations of arbitrage theory. We will explore models for more complicated situations, including incomplete markets and dynamic optimization. The theoretical material will be accompanied by tutorials on relevant computational and statistical techniques.

MATH 5075/5076 is a required sequence for Master's students in the School of Mathematics for the financial mathematics specialization.

The course covers tools and techniques for building robust financial models using the Python programming language. Python topics: language features, scientific computing packages, OOP, design patterns, network programming, unit testing, and custom packaging. Ancillary development topics: Jupyter notebooks, Visual Studio Code, Git, Docker, and time series databases. Students will apply their technical skills in a quant finance context, along the way learning: financial time series analysis and forecasting, trading system development, numerical equity derivative pricing, and risk management.

Building directly on FM 5151, this course develops the professional software engineering skills that quantitative finance roles demand. Students design and implement a near-production-scale Monte Carlo simulator for pricing exotic derivatives in C#, covering data modeling and implementation in SQL and API design along the way. The capstone project brings these skills together: a portfolio management tool built to trading-desk standards.

This course introduces the basic principles underlying Data Science and Machine Learning, focusing on their applications in finance. Topics include: understanding data, EDA, various types of Machine Learning problems (e.g. classification, regression, recommendation, etc.), various algorithmic approaches (GLMs, Trees, Neural Networks, etc.), model selection, limitations of ML models, and issues in their implementations.

Topics include: Taxonomies of Risk, Measures of Risk, Risk Modeling, and Risk Mitigation strategies. Additionally, the role and purpose of Risk Management will be discussed

This elective on fixed income markets expands on the basic concepts in the core curriculum and provides students a deeper understanding of this market through a hands-on approach.

A practical course exposing students to a variety of trading strategies used in Hedge Funds.

This elective’s focus is optimization techniques and their applications in portfolio management. The emphasis is on theory and how it is used in practice.    

This elective focuses on the stylized facts in market microstructure and its application in algorithmic trading. In order to deal with the vast amount of real time streaming data in algorithmic trading, students will learn how to use KDB+ (a time series database) and its language q (a vectorized functional language).

This course introduces the fundamentals of Deep Learning with practical applications, focusing on implementation using PyTorch. Topics include the mechanics of deep learning, optimization basics, and neural network architectures such as fully connected, convolutional, and recurrent networks. Students will also explore modern training techniques, advanced network components, and best practices for improving model performance. Hands-on projects and examples from financial applications will reinforce key concepts.