The field of mathematical finance is comparatively young, and the modern theory can be traced back to the Black-Scholes-Merton solution of the problem of how to price a call option, a financial security whose payoff is contingent on the behaviour of an underlying asset. Over the past three decades the explosive growth in trading of financial derivatives has been reflected in a commensurate growth in the study of financial mathematics, which in turn has helped to support the increasing sophistication of financial markets.
As a branch of mathematics, finance is extremely diverse, and the subject has attracted the interest of, and generated research problems for, researchers from a broad spectrum of mathematical disciplines. The theory is based on stochastic models, and there are obvious applications from statistical analysis, but there have also been significant contributions from functional and convex analysis. There are also strong connections with numerical analysis and computational methods, not least because many of the equations which arise have long been studied by applied mathematicians. The healthy development of the subject also needs input from economists and industry professionals.
The major themes of this programme are asset price modelling and inference for financial models; market imperfections and derivative pricing in incomplete markets; insurance applications and the modelling and quantification of credit events; computational finance; and financial economics and agent interactions. The aim is that researchers from all related disciplines - from economics, physics and finance as well as pure and applied mathematics and statistics - should meet and interact, to share knowledge and advance understanding.