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.
Email: gberkolaiko@tamu.edu
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.
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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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