Design and analyze algorithms, including dynamic structures maintenance and hashing, searching, sorting, and traversal. Examine time and space requirements; simplification; computational complexity; proof theory and testing; NP–hard and NP–complete problems.
Develop term structure models and options based on fixed–income securities, including standard lognormal models, short–term interest rate models, and more complex derivative models.
Discuss advanced topics in derivative securities to extend content and concepts presented within the introduction to derivatives and fixed income courses. Develop numerical techniques used to implement pricing methodologies, term structure models, and options based on fixed income securities.
Examine knowledge–based systems design and implementation; expert systems shells and programming environments. Apply skills to the validation and implementation of expert systems.
Numerical Methods I
Learn numerical and computational aspects of various mathematical topics: finite precision, solutions of non–linear equations, interpolation, approximation, linear systems of equations, and integration.
Numerical Methods II
Learn and apply further techniques of integration, ordinary differential equations, numerical linear algebra, nonlinear systems of equations, boundary value problems, and optimization.
Partial Differential Equations
Learn Fourier series and applications to solutions of partial differential equations. Includes separation of variables, eigenfunction expansions, Bessel functions, Green’s functions, Fourier and Laplace transforms.
Quantitative Finance Capstone
Integrate skills and knowledge from prior program coursework to develop a topic of special interest. Includes a comprehensive examination during which students present and discuss their final project.
Quantitative Methods in Finance
Emphasizes the mathematical structure of and methods for model solutions in asset and derivative pricing, capital budgeting and real options, financing, and liquidity. Includes solutions of systems of equations, complementarity, and optimization. Applications of numerical analysis, integration and differentiation, and functional and differential equation solutions.
Uncertainty Analysis and Measurement
Examines the nature and importance of modeling and measuring uncertainty; theoretical and computational approaches to modeling and measuring uncertainty; qualitative and quantitative uncertainty modeling and measurement; computational issues in uncertainty modeling and measurement; simulation, moment generating and characteristic probability functions.
Topics in Quantitative Finance
Offered as an independent study opportunity. Research, study, and discuss topics of special interest under the guidance of a member of the faculty.
Readings in Quantitative Finance
Offered as an independent study opportunity for qualified students. Study and discuss selected readings under the guidance of a member of the faculty.