Mathematical Sciences
Courses
MA 611 Analysis of Financial Time Series (3 credits)
Pre- or corequisite(s): ST 625. Recommended: MA 631
Examines methods for analyzing financial time series. In many times series, observations from different times periods are correlated, which implies a treatment that is different from usual regression analysis methods. The course reviews regression, smoothing and decomposition time-series models, introduces Box-Jenkins analysis and its extensions, and other modeling techniques commonly used in finance, such as quantile estimation and value at risk, duration models and the analysis of panel data.
MA 631 Mathematical Foundation of Quantitative Finance (3 credits)
Prerequisite(s): Advanced math background critical
Provides the mathematical tools necessary for an in-depth study of quantitative finance. The major topic areas covered are: single and multivariate calculus, continuous probability, Brownian motion stochastic process and Ito calculus. the course focus is on developing the mathematical tools necessary for understanding financial models based on the Ito calculus.
MA 639 Asset Valuation and Derivative Pricing (3 credits)
Prerequisite(s): MA 631
Applies mathematical methods presented in MA 631 to a particularly important set of problems in finance, namely, the valuation of assets and the pricing of derivatives. The course focuses on pricing and hedging of financial derivatives within basic discrete and continuous time models of financial markets. Real market data is used for homework assignments and a course project. Along with the standard probability and calculus tools, discrete and continuous time martingales, partial differential equations, stochastic differential equations, and Ito calculus are used in the course.
MA 710 Data Mining (3 credits)
Prerequisite(s): ST 612 or ST 625 or Instructor Permission
This course will introduce participants to the most recent data mining techniques, with an emphasis on: getting a general understanding of how the method works, understanding how to perform the analysis using suitable available software, understanding how to interpret the results in a business research context, and developing the capacity to critically read published research articles which make use of the technique. Contents may vary according to the interest of participants.
Topics may include decision trees, an introduction to neural nets and to self organizing (Kohonen) maps, multiple adaptive regression splines (MARS), an introduction to genetic algorithms, to association (also known as market basket) analysis, to web mining and text mining, and to social networks.
MA 731 Applied Modeling (3 credits)
Prerequisite(s): MA 631; Intended to be taken immediately after MA 631.
This course is an introduction to the practical issues related to the computer implementation of financial models built on stochastic differential equations. Techniques explored will include stochastic process simulation and estimation, computation of sample path solutions to stochastic differential equations, and efficient estimation of path dependent conditional expectations. Application areas will include computer implementation of asset valuation and term structure models. Students will use mathematical software for comparative analyses of numerical algorithms.
