Mathematical Finance and Actuarial Science
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. 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.
Peter is the Head of the School of Mathematics, his research interests include Computational and Asymptotic Fluid Dynamics, High Reynolds Number Flows, Hydodynamic instability and transition and Mathematical Finance. He uses a combination of analytical and computational methods, the one informing the other. For example, accurate numerics can give guidance as to the topology and structure of solutions, for example singularities, which can then point the way to an analytic description. Equally asymptotic methods can be used in formulating, for example, far-field boundary condition, which can then be used to make numerical schemes more efficient.
Paul is a Lecturer in Financial Mathematics, he works as part of the Mathematical Modelling in Finance and Economics Group in which they model financial systems with uncertain price and uncertain physical flow, leading to non-linear PDEs which must be solved numerically. He has investigated such systems in the world of mining, working with the international leading mining software company Gemcom, and also within the framework of Revenue Management systems, working with the local business Inventive IT.