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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 earlier work in numerical analysis was on 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 earlier publications.
Analytical Solution of a class of network dynamics with mechanical and financial applications (with Pavel Krejčí, Sergei Melnik and Dmitrii Rachinskii). Phys Rev E 90, 032822 (2014). PDF file
Implausible Equilibrium Solutions in Economics and Finance PDF file
Kurzweil Integral representation of interacting Prandtl-Ishlinskii Operators (with Pavel Krejčí, Sergei Melnik and Dmitrii Rachinskii), Dsc. Cont. Dyn Sys (20) pp 2949-2965 (2015). PDF file
The Kurzweil Integral in Financial Market Modeling (with Pavel Krejčí, Giselle Antunes Monteiro and Dmitrii Rachinskii) PDF file . Mathematica Bohemica (141) pp 261-286 (2016)
Dynamics of Discrete Time Systems with a Hysteresis Stop Operator (with Maxim Arnold, Nikita Begun, Pavel Gurevich, Eyram Kwame and Dmitrii Rachinskii) PDF file . Submitted to SIAM J. Applied Dynamical Systems.The transition from Brownian motion to boom-and-bust dynamics in financial and economic systems PDF file . To appear, Computational Economics and Finance.
Rational and Boundedly Rational Inaction in a Macroeconomic Model (with Eyram Kwame, Pavel Krejčí and Dmitrii Rachinskii) PDF file . Submitted.
A continuum of path-dependent equilibrium solutions induced by sticky expectations (with Pavel Krejčí, Dmitrii Rachinskii, Eyram Kwame and Andrei Zagvozdkin) PDF file . To appear.
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)