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- Visiting Professor
- Dept of Mathematics
- Faculty of Maths & Physical Sciences
I carry out research both in mathematical finance and in mathematical physics. My research in financial mathematics is in the general area of stochastic models for the dynamics of asset prices and related derivatives. I have worked on the development of mathematical models for the dynamics of interest rates, foreign exchange, equities, credit, commodities, and inflation, with applications (a) to the pricing and risk management of derivatives, and (b) to the formulation of optimal investment strategies. My more recent work includes papers with various collaborators on topics such as Wiener chaos methods as a basis for financial modelling, discrete-time interest rate theory, monetary models for inflation, Lévy models for jumps in asset prices, information-based asset pricing, signal processing with Lévy information, aggregation of risk aversion in heterogeneous financial markets, and the asymptotic properties of interest rate systems.
My work in mathematical physics has resulted in papers spanning a range of topics including, in particular, cosmology, general relativity, twistor theory, statistical mechanics, quantum statistical inference, quantum information, and quantum measurement. In recent years my research in mathematical physics has been focused on various aspects of the mathematical foundations of quantum theory, with an emphasis on the use of methods of algebraic geometry and stochastic analysis, and with a view towards applications to quantum information processing and quantum tomography.