# MATH 628 - Mathematics of Finance - Fall 2022

** Credits 3. 3 Lecture Hours. **

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; application of probability topics including conditional expectations, Markov chains and Martingales, extreme value theory; applications in optional stopping theorem and trading strategies, Markov Chains in credit risk modeling. **Prerequisite:** MATHÂ 251 and MATHÂ 411, or equivalent, or approval of instructor.

### Sections

Sec | Instructor | Lecture | |
---|---|---|---|

600 |
Berkolaiko,Gregory | T R 12:45-14:00 BLOC 160 |