Twin Cities campus

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Twin Cities Campus

Financial Mathematics Minor

School of Mathematics
College of Science and Engineering
Link to a list of faculty for this program.
Contact Information
Program in Financial Mathematics, 127 Vincent Hall, 206 Church Street SE, Minneapolis, MN 55455 (612-624-6391; fax: 612-624-6702)
Email: mcfam@umn.edu
Website: https://cse.umn.edu/mcfam/
  • Program Type: Graduate minor related to major
  • Requirements for this program are current for Fall 2023
  • Length of program in credits (master's): 8
  • Length of program in credits (doctoral): 12
  • This program does not require summer semesters for timely completion.
The graduate minor in Financial Mathematics exposes students to the interdisciplinary field of quantitative finance. The courses in the program feature a blend of theory and practice, covering topics in mathematics, statistics, data science, machine learning, and modeling and programming in the context of finance and financial risk management. Courses are taught by practitioners, helping students develop skills that are attractive for employment in the broad area of quantitative finance. Minor course plans will be tailored for each student’s individual background and goals. Courses are offered in the evenings to accommodate working professionals.
Program Delivery
  • via classroom (the majority of instruction is face-to-face)
Prerequisites for Admission
Special Application Requirements:
Students interested in the minor are strongly encouraged to confer with their major field advisor and director of graduate studies, and the MCFAM academic director to determine which courses match the student's knowledge, skills, and professional goals.
For an online application or for more information about graduate education admissions, see the General Information section of this website.
Program Requirements
Use of 4xxx courses towards program requirements is not permitted.
Courses offered on both the A-F and S/N grading basis must be taken A-F, with a minimum grade of B earned for each course. The minimum cumulative GPA for the minor is 3.00.
Minor Coursework (8-12 credits)
Master's students select 8 credits, and doctoral students select 12 credits from the following in consultation with the MCFAM academic director:
FM 5111 - Introduction to Financial Markets (3.0 cr)
FM 5121 - Mathematics for Finance (3.0 cr)
FM 5151 - Financial Modeling I: Python (3.0 cr)
FM 5212 - Continuous Time Finance (3.0 cr)
FM 5222 - Statistical Methods in Finance (3.0 cr)
FM 5252 - Financial Modeling II: Numerical Methods and Simulations (3.0 cr)
FM 5323 - Data Science and Machine Learning in Finance (3.0 cr)
FM 5343 - Quantitative Risk Management (3.0 cr)
FM 5353 - Software Development in Finance (3.0 cr)
FM 5411 - Fixed Income Market (2.0 cr)
FM 5422 - Quantitative Hedge Fund Strategies (2.0 cr)
FM 5432 - Portfolio Optimization (2.0 cr)
FM 5462 - Market Microstructure (2.0 cr)
FM 5990 - Topics in Financial Mathematics (1.0-2.0 cr)
FM 5993 - Directed Study in Financial Mathematics (1.0-2.0 cr)
Program Sub-plans
Students are required to complete one of the following sub-plans.
Students may not complete the program with more than one sub-plan.
Masters
Doctoral
  
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FM 5111 - Introduction to Financial Markets
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
This course is a survey of important elements of financial markets and setting the context to the program. Topics include Complete vs incomplete markets, financial institutions, traded instruments, elements of accounting, arbitrage, Fundamental Theorem of Asset Pricing, Credit, Investment and Risk Management.
FM 5121 - Mathematics for Finance
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
This course establishes the mathematical foundation needed for modeling in finance, with focus on probability and statistics, stochastic processes, linear algebra, and more.
FM 5151 - Financial Modeling I: Python
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
This course establishes the basic principles of Financial Modeling. Topics include different kinds of models (e.g. descriptive vs explanatory, statistical vs structural, etc.), foundational models used in finance (binomial, lognormal, Gaussian, etc.) and their applications (stocks, interest rates, commodities, etc.). Python will be used extensively to illustrate the models, therefore this course also serves as an introduction to the use of Python in finance.
FM 5212 - Continuous Time Finance
Credits: 3.0 [max 3.0]
Typically offered: Every Spring
A course on Stochastic Calculus - based modeling in finance, focusing on the Black-Scholes model and its extensions.
FM 5222 - Statistical Methods in Finance
Credits: 3.0 [max 3.0]
Typically offered: Every Spring
A course on Statistical methods used in the analysis of financial markets data. It will cover topics such as, Bayesian Statistics, Linear and Non-Linear Regression, Markov Chain Monte Carlo, Copulas and Time-series Analysis, and their applications to financial data.
FM 5252 - Financial Modeling II: Numerical Methods and Simulations
Credits: 3.0 [max 3.0]
Typically offered: Every Spring
This course focuses on Monte Carlo simulations and elements of scientific computing as tools in modeling. These methods will be used as a key technique to develop and assess models, and considerable time will be spent on the interpretation of model outputs.
FM 5323 - Data Science and Machine Learning in Finance
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
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.
FM 5343 - Quantitative Risk Management
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
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.
FM 5353 - Software Development in Finance
Credits: 3.0 [max 3.0]
Typically offered: Every Fall
This class introduces the toolset of a compiled language and principles of object-oriented programming. Databases are introduced and data models related to finance applications are explored. Projects are sourced from applied finance problems and are implemented with a focus on performance and common practices in professional software development.
FM 5411 - Fixed Income Market
Credits: 2.0 [max 2.0]
Typically offered: Periodic Fall
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.
FM 5422 - Quantitative Hedge Fund Strategies
Credits: 2.0 [max 2.0]
Typically offered: Periodic Spring
A practical course exposing students to a variety of trading strategies used in Hedge Funds.
FM 5432 - Portfolio Optimization
Credits: 2.0 [max 2.0]
Typically offered: Periodic Spring
This elective?s focus is on optimization techniques through the development of an appropriate mathematical framework as well as their applications in portfolio management. The course will have a particular emphasis in convex optimization and practical pitfalls in application. Students will solve both mathematical problems in the area as well as implement solutions with real market data. The elective will conclude with a group project where students will work with market data and analyze implementations of drawdown and conditional value-at-risk optimizations with equity returns under turnover constraints.
FM 5462 - Market Microstructure
Credits: 2.0 [max 2.0]
Typically offered: Periodic Spring
This course 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).
FM 5990 - Topics in Financial Mathematics
Credits: 1.0 -2.0 [max 6.0]
Typically offered: Periodic Fall & Spring
The course will focus on a special topic in quantitative finance that supplements the regular curriculum of the Master of Financial Mathematics program. The course features experts, often finance industry practitioners, who share their experience and knowledge. prereq: enrolled in the Master of Financial Mathematics program or instr consent
FM 5993 - Directed Study in Financial Mathematics
Credits: 1.0 -2.0 [max 6.0]
Typically offered: Periodic Fall & Spring
A course in which a student is conducting a directed study or a research project under the direction of a faculty member / program instructor. Can be repeated.