My PhD thesis, entitled Integral Bases of Dihedral Number Fields was supervised by Walter Ledermann at the Universty of Sussex. After a post-doc at the Universty of Amsterdam, a rather tortuous year as a bond analyst for Phillips and Drew and a delightful Masters in Mathematical Economics and Econometrics at the London School of Economics, I returned to Sussex as a lecturer in Mathematics and Economics. That was in 1985, by which time my research interests had turned to game theory.


However, after the 1987 Black Monday crash in global financial markets my econometric skills were in greater demand, and my social conscience drew me away from game theoretic research into something more practical. I undertook various consultancy roles for investment banks and other financial institutions, where I worked with computer programmers to implement models for risk analysis and portfolio management. This way, I became drawn to research in financial risk management, investigating the properties of various new econometric models for market risk including different types of generalised autoregressive conditional heterscedasticity (GARCH) models , as well as applied research on active and passive fund management. From that time on, almost all my research has been with the wonderful PhD students that I have had the privilege to supervise.


Further econometric research on estimation of general discrete-time stochastic processes for financial asset returns naturally shifted my attention towards the implied measure, at which point I necessarily became a rather inefficient autodidact in various elements of mathematical finance. In this sphere I developed pricing and hedging models for various types of options, exotic and otherwise, and with two very talented PhDs we proved some classic theoretical results on scale invariance and generalised aggregation properties. Likewise, more applied mathematical finance research converged on volatility indices and higher moment risk premia, and on trading these premia through futures and exchange traded products.


While writing my 4-volume textbook Market Risk Analysis (Wileys, 2008) Walter Ledermann was interested to read parts of the first volume Quantitative Methods in Finance. In his early career as a young mathematician in Edinburgh Walter had done some interesting research on correlation matrices, and after reading my textbook he proved the last theorem of his life at the age of 97. By coincidence, I was supervising the PhD of his grandson at the time. Together Dan, Walter and I wrote the first paper on random orthogonal matrix (ROM) simulation, timing the publication for the centenary of Walter's birth. In his honour, we named the Ledermann matrix that Walter discovered as the first in a whole class of L-matrices that Dan and I developed. I continue to work on ROM simulation and have also developed another new type of simulation model based on factor quantiles.

Currently, the main focus of my research is on the exciting new universe of crypto assets and their derivatives.