Mathematical Finance is a very active branch of both Probability Theory and Applied Mathematics. It is probably one of the few areas in academic research which interact constantly with their field of application and with a huge impact on the daily functioning of the world's financial institutions.
Mathematical Finance was born in 1900 with the doctoral dissertation Théorie de la speculation by Louis Bachelier. After a long gap, the Nobel laureate Paul Samuelson deepened and extended Bachelier's idea in the 1960s. Both works were based on or related to the Wiener process, the most important representant of a stochastic process. These ideas led finally to the central result of modern finance in 1973, the Black-Scholes formula which gives the price of a derivative and which was worth another Nobel prize in 1997.
One of the cornerstones of Mathematical Finance is Stochastic Calculus. Originally, Black, Scholes and Merton used partial differential equations to derive their pricing formula. Nowadays, tools from Stochastic Calculus, in particular martingales, are also used to price derivatives.
Another cornerstone in Mathematical Finance is the theory of Stochastic Differential Equations. Not only in Mathematical Finance but also in many other disciplines, the change of a state can not only be described by a deterministic equation but one also has to take into account some random perturbations.
Mathematical Modelling in Finance and Economics
The Mathematical Modelling in Finance and Economics Group was established in 1999 after Peter Duck from the School of Mathematics and David Newton, then of Manchester Business School, agreed to co-supervise two PhD students. This mixing of mathematics and business resulted in innovative research. This interdisiplinary and applied approach to the subject has continued with a steady stream of PhD students.
We now have four academics members who work in this area: Peter Duck, Geoffrey Evatt, Paul Johnson and Sydney Howell (Manchester Business School). We also collaborate with other academics in the School, such as John Moriarty and Goran Peskir from the Probability Group, and with colleagues from other Schools such as the Business School, School of Electrical and Electronic Engineering, and School of Physics.
We have strong links with industry and are interested in any problem in which the models and techniques from Mathematical Finance might be applied. Some examples of the more interesting research topics investigated by the group are highlighted in our applied research topics page.