Financial Mathematics has emerged over the last 40 years as a new and vigorous scientific discipline. It started as a collection of techniques from applied mathematics arising out of macroeconomics and microeconomics, but is now a systematic study of mathematical models and their analysis as they apply to problems in financial risk management. Because of the complexity of market forces, those working in this field require an extensive mathematical and statistical background. Theoretical developments are almost immediately implemented in the financial sector since the financial instruments are constantly evolving.
There are a number of graduate programs in North America, most of which have started in the last five years (some can be accessed by clicking here). However, the models and their analysis, to a significant extent, rely on undergraduate-level mathematics such as calculus, measure theory, numerical analysis, stochastic processes, linear algebra, probability and differential equations. Our programs include these fundamental mathematical theories which are then given concrete meaning through the simultaneous development of appropriate financial applications. Laboratory experience with computational mathematics in the context of these applications is essential for a comprehensive study of this field and is included as well. The BA and BSc programs provide not only the skills necessary for immediate application but also the understanding needed to continue to acquire and develop new techniques.
Our "financial mathematicians" are well-prepared to adapt to changes in this rapidly evolving field. The same theory and methods are being used throughout the world, so employment opportunities are truly global. The programs have as their fundamental core rigorous mathematics training so that outstanding students will be well-suited to graduate work in either financial mathematics or in more pure mathematics.
Harry Markowitz's 1990 Nobel Prize winning work on Portfolio Selection introduced the concept of a minimum variance strategy by quantifying diversification in a market. Markowitz shared the Nobel prize with William Sharpe, who developed covariance strategies in the selection of stocks, allowing the use of optimization methods in financial analysis. Merton M. Miller shared in the 1990 Prize for his work related to capital structure and dividend policy. In 1973, Fisher Black and Myron Scholes derived the famous Black-Scholes formula involving the partial differential equation formulation of the value of the European call option, and this work was extended by Robert Merton in the same year. Scholes and Merton were awarded the 1997 Nobel Prize in Economics for this foundational work. Today, Brownian-motion models are the norm for financial markets. The popularity of derivatives and synthetics is driving a continued growth in sophisticated risk management strategies and, increasingly, banks and corporations rely on in-house experts for quantitative financial analysis. It is no longer sufficient to have a working knowledge of the theory of interest: concepts in securities, portfolio selection and modern methods of analysing financial data require a comprehensive program of study in advanced mathematics.