AMS 691, Topics in Applied Math
Varying topics selected from the list below if sufficient interest is shown. Several
topics may be taught concurrently in different sections: Advanced Operational Methods
in Applied Mathematics, Approximate Methods in Boundary Value Problems in Applied
Mathematics, Control Theory and Optimization Foundations of Passive Systems Theory,
Game Theory, Mixed Boundary Value Problems in Elasticity, Partial Differential Equations,
Quantitative Genetics, Stochastic Modeling, Topics in Quantitative Finance.
OFFERED FOR FALL 2019 SEMESTER ONLY:
AMS 691.01 Topics in Applied Mathematics (
Quantitative Finance Case Studies: Advanced Statistics):
Introduction to most commonly used interest rate models: Heath-Jarrow-Morton, Brace-Gatareck-Musiela,
etc. Cap, Floor, Euopean and Bermudan option pricing. Credit modeling: Merton structural
approach vs. Intensity approach. Corporate bonds, CDS, securitized products (CDO,
CLO, mortgages), Credit value adjustment (CVA, XVA).
Credits: 0 - 3
The course notes cover the main material of the course. For better understanding of
material, it is suggested to read original articles containing relevant material.
Supplemental reading: Zabarankin, M. and S. Uryasev. “Statistical Decision Problems.
Selected Concepts and Portfolio Safeguard Case Studies.” Optimization and Its Applications,
Vol. 85, Springer, 2014; ISBN: 9781493953257 (paperback)