Course Descriptions
Computer Science
CS 522 Data Mining
Financial Markets
FM 492 Introduction to C/C++ Programming for Financial Markets
FM 530 Visual Basic and Databases for Financial Markets
Math
MATH 481 Introduction to Stochastic Processes with Applications
MATH 485 Introduction to Mathematical Finance
MATH 486 Mathematical Modeling I
MATH 512 Partial Differential Equations
MATH 513 PDEs for Finance*
MATH 542 Stochastic Processes
MATH 543 Introduction to Stochastic Analysis
MATH 544 Stochastic Dynamics
MATH 565 Monte Carlo Methods in Finance
MATH 582 Mathematical Finance*
MATH 583 Quantitative Modeling of Derivative Securities
MATH 584 Mathematical Portfolio and Investment Theory*
MATH 586 Theory and Practice of Fixed Income Modeling*
MATH 587 Theory and Practice of Modeling Credit Risk and Credit Derivatives*
MATH 589 Numerical Methods for PDEs
Finance
MSF 521 Financial Modeling I
MSF 522 Financial Modeling II
MSF 551 Futures, Options and OTC Derivatives
MSF 561 Financial Time Series Analysis
MSF 562 Econometric Analysis
MSF 571 Computational Finance I
MSF 572 Computational Finance II
MSF 573 Computational Finance III
CS 522 Data Mining
This course provides continued exploration of data mining algorithms. More sophisticated algorithms such as support vector machines will be studied in detail. Students will continuously study new contributions to the field. A large project will be required that encourages students to push the limits of existing data mining techniques. (Prerequisite: CS 422)
FM 492 Introduction to C/C++ Programming for Financial Markets
This course presents the ANSI C++ programming language. Students will study program design, including functions, arrays and strings, pointers, dynamic memory management, data structures and the Standard Template Library. Object-oriented design will be discussed, including the design and use of classes, overloading, inheritance and polymorphism. The focus will be to understand OOP concepts as they are applied to financial markets.
FM 530 Visual Basic and Databases for Financial Markets
The course is designed to provide students with a comprehensive knowledge of the VB.NET programming environment that includes object oriented design using the .NET Framework. It will also cover relational database design, SQL, XML and the Unified Modeling Language. These tools will be used to create financial models using real time and historical market data. Students will develop financial applications using advanced Visual Basic tools. (Prerequisite: FM 506.)
MATH 481 Introduction to Stochastic Processes with Applications
This is an introductory course in stochastic processes. Its purpose is to introduce students into a range of stochastic processes, which are used as modeling tools in diverse fields of applications, especially in business applications. The course introduces the most fundamental ideas in the area of modeling and analysis of real World phenomena in terms of stochastic processes. The course covers different classes of Markov processes. It also presents some aspects of stochastic calculus with emphasis on the application to financial modeling and financial engineering. (Prerequisite: MATH 332 or MATH 333, MATH 475)
MATH 485 Introduction to Mathematical Finance
This is an introductory course in mathematical finance. Technical difficulty of the subject is kept at minimum by considering a discrete time framework. Nevertheless, the major ideas and concepts underlying modern mathematical finance and financial engineering will be explained and illustrated.
MATH 486 Mathematical Modeling I
This course is a general introduction to optimization problems. Linear programming: the simplex method. Elements of graphs and networks. Introduction to game theory. Applications. (Prerequisite: MATH 475 or instructor�s consent)
MATH 512 Partial Differential Equations
This course covers basic model equations describing wave propagation, diffusion and potential functions. Fourier transform, Green�s functions, eigenfunction expansions, perturbation techniques, multiple-scale methods, asymptotics, variational techniques, self-similar solutions. Prerequisite: MATH 400 or instructor�s consent.
MATH 513 PDEs for Finance*
This course provides an introduction to those aspects of partial differential equations and optimal control most relevant to finance. Linear parabolic PDEs and their relations with stochastic differential equations: the forward and backward Kolmogorov equation, exit times, fundamental solutions, boundary value problems, maximum principle. Deterministic and stochastic optimal control: dynamic programming, Hamilton-Jacobi-Bellman equation, verification arguments, optimal stopping. Applications to finance � including portfolio optimization and option pricing�are distributed throughout the course.
MATH 542 Stochastic Processes
This is an introductory course in stochastic processes. Its purpose is to introduce students into a range of stochastic processes, which are used as modeling tools in diverse fields of applications, especially in the risk management applications for finance and insurance. In addition, students will be introduced to some basic stochastic analysis.
MATH 543 Introduction to Stochastic Analysis
This course will introduce modern finite dimensional stochastic analysis and its applications in finance and insurance. The topics will include: (a) an overview of modern theory of stochastic processes, with focus on semimartingales and their characteristics; (b) stochastic calculus for semimartingales, including Ito formula and stochastic integration with respect to semimartingales; (c) stochastic differential equations (SDEs) driven by semimartingales, with focus on stochastic SDEs driven by Levy processes; (d) absolutely continuous changes of measures for Semimartingales, (e) some selected applications.
MATH 544 Stochastic Dynamics
This is an introductory course in mathematical modeling by stochastic differential equations. It is especially appropriate for graduate students who would like to use stochastic methods in their research, or to learn these methods for long-term career development. Topics include random variables, mean and variance, Brownian motion, stochastic integration and Ito calculus, stochastic differential equations, random dynamics, numerical simulation, and applications to scientific, engineering and financial problems. Prerequisite: MATH 474, MATH 475 or equivalent.
MATH 565 Monte Carlo Methods in Finance
In addition to the theoretical constructs in financial mathematics, there is also a range of computational techniques that allow for the numerical evaluation of a wide range of financial securities. Monte Carlo and Quasi Monte Carlo techniques are computational sampling methods which track the behavior of the underlying securities in an option or portfolio and determine the derivative�s value by taking the expected value of the discounted payoffs at maturity. Recent developments with parallel programming techniques and computer clusters have made these methods widespread in the finance industry.
MATH 582 Mathematical Finance*
This course will introduce the student to modern continuous time mathematical finance. The major objective of the course is to present main mathematical methodologies and models underlying the area of financial engineering, and, in particular, those that provide a formal analytical basis for valuation and hedging of financial securities.
MATH 583 Quantitative Modeling of Derivative Securities
This course makes a connection between theory and application of mathematical finance and financial engineering.
MATH 584 Mathematical Portfolio and Investment Theory*
This course provides a mathematical view of mathematical theory and practice of optimal asset allocation.
MATH 586 Theory and Practice of Fixed Income Modeling*
The course covers basics of the modern interest rate modeling and fixed income asset pricing. The main goal is to develop a practical understanding of the core methods and approaches used in practice to model interest rates and to price and hedge interest rate contingent securities. The emphasis of the course is practical rather than purely theoretical. A fundamental objective of the course is to enable the students to gain a hand-on familiarity with and understanding of the modern approaches used in practice to model interest rate markets.
MATH 587 Theory and Practice of Modeling Credit Risk and Credit Derivatives*
This is an advanced course in the theory and practice of credit risk and credit derivatives.
MATH 589 Numerical Methods for PDEs
Finite difference method, finite volume method, spectral method; order of accuracy, stability and Fourier analysis of numerical schemes.
