MATH 628: Mathematical tools in finance

Fall 2023

Course Homepage: Canvas


Advanced Linear Algebra: orthogonality and projections, eigenvalue and SV decomposition, pseudoinverse, least squares and minimum norm solutions, hyperplane separation theorem; applications to Mean-Variance Portfolio Analysis and Capital Asset Pricing Model, Arbitrage and Fundamental Theorem of Asset Pricing, 1-period asset replication in incomplete markets. Optimization and Calculus of Variations: Lagrange multipliers, dynamical programming, numerical methods; applications to Utility Theory, multi-period asset replication in incomplete markets. Applied Probability topics: Conditional expectations, Markov chains and Martingales, Extreme Value Theory; applications to: Optional Stopping Theorem and trading strategies, Markov Chains in credit risk modeling. Prerequisites: Multivariate Calculus (MATH 251 or equivalent); Probability (MATH 411 or equivalent) or MSQF Bootcamp. Recommended: MATH 425 (concurrent enrollment ok).


Learn or refresh the mathematical tools that are commonly used in Finance classes (at Masters or PhD level) and finance applications: advanced linear algebra, optimization and applied probability.


3 credits


The following book provides an excellent blend of mathematics with immediate links to finance applications. The course will cover most of it.

Lecture notes or freely-accessible sources will be provided for the mathematical topics that will be explored deeper in the course.

Among books more focused on applications are


Dr Gregory Berkolaiko, Blocker 625c.


TR 12:45-2:00, BLOC 128.


Mondays 3-4, Friday 11-noon and by appointment.


Homework will be posted on the course homepage, approximately every 3 weeks.


Students are expected to actively participate in the class: attend the lectures, ask questions when lost, and answer the instructor's questions.


The following grade breakdown will be used:
Grade Percentage   Grade Ingredients:
A 85% and more
B 70% and more Homeworks 80%
C 55% and more Class Participation 20%
D 40% and more
F less than 25%



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This file was last modified on Monday, 21-Aug-2023 18:20:18 CDT.