Mathematical Methods For Finance

This course is an introduction to mathematical finance. The course serves to equip students with basic mathematical knowledge and computational skills needed to solve problems related to finance. Furthermore, this course lays the foundation for more advanced topics, such as econometrics, stochastic calculus and optimal control theory, which make finance a very exciting subject. Modern finance draws upon many fields of mathematics, in particular, algebra, econometrics, numerical analysis, optimization theory, partial differential equations, probability theory, statistics and stochastic calculus. The diversity of mathematical skills needed to master finance makes it a very challenging subject for students. The mathematical topics covered in this course include matrix algebra, calculus, difference equation, differential equation, optimization and portfolio mathematics (please refer to the proposed seminar schedule for details). The topics in the first five weeks of the course introduce students to the simplest financial market model and explain arbitrage pricing in a discrete time framework. The topics in the next three weeks lay the foundations for continuous time finance. The topics in the last four weeks introduce students to optimization and portfolio theory. These selected topics serve as an introduction to some of the fields of mathematics that modern finance draws upon.