If you are one of my current students then you may be looking for information found here:
My research on dynamical systems has included work on vibro-impacting systems, population dynamics, nonlinear phenomena in power networks and economic modelling. The common theme in all of the above is the presence of discontinuities in the mathematical models.
My work in numerical analysis has been the analysis and development of adaptive timestepping algorithms for both Ordinary and Stochastic Differential Equations.
Recent work in the area of economics and financial modelling has focused on the development and analysis of mathematical models that operate under more realistic assumptions than those used in neoclassical economics. In particular we attempt to mimic the ways in which human psychology and institutional market defects (such as herding, moral hazard and perverse incentives) affect financial markets.
I co-organized a 3 week-long workshop in Glasgow in June 2009 on `The Limits to Rationality in Economics and Financial Markets' as well as a shorter one in January 2009 restricted to memory effects in economics. More details can be found here
You can download recent preprints in PDF format below. Click here for links to, or copies of, selected publications.
Market statistics of a psychology-based heterogeneous agent model (with Tim Seaman, to appear Int. J. Theor. Appl. Fin.) PDF file
Stepsize control for the Milstein scheme using first-exit-times PDF file
Rational Expectations, psychology and inductive learning via moving thresholds (with Tim Seaman). To appear Phys. A. PDF file
Hysteresis and Economics (with Rod Cross and Michael Grinfeld , to appear IEEE Control Systems Magazine) PDF file
A queueing theory description of fat-tailed price returns in imperfect financial markets (to appear, Eur. Phys. J. B). PDF file
How sensitive are equilibrium pricing models to real-world distortions? PDF file
A Mesoscopic Market Model with Hysterestic Agents (with Rod Cross and Michael Grinfeld PDF file
Centre for Mathematical Sciences, University of Cambridge, UK (Undergraduate and Part III)
Department of Mathematics, University of
Bristol, UK (PhD)
Department of Mathematics, University of Strathclyde, UK (Post-doctoral position)
Scientific Computing and Computational Mathematics Program, Stanford University, USA (Post-doctoral position)