Preface
There is money to be made in the financial industry. Academics, under pressure to exhibit relevance, are happy to point to their consultancies in the City as evidence of their value in the market, and the industry has shown a notable ability to recruit the brightest and best from our Universities. These observations should not obscure the profound scientific challenges posed by the area of finance. The area has both stimulated and benefited from advances in a range of mathematical sciences, most obviously probability, differential equations, optimization, statistics and numerical analysis. One thinks, for example, of Bernoulli’s resolution, in the 18th century, of the St Petersburg Problem through his introduction of a logarithmic utility, of Bachelier’s description, at the turn of this century, of the stochastic process we now call brownian motion, of Kendall’s investigation, forty years ago, of the statistical unpredictability of stock prices, and of the current enormously fertile interaction between economics and mathematics centred around martingale representations. Looking to the future, some of the mathematical ideas originally motivated by statistical mechanics, and since used to model the large-scale telecommunication networks upon which the financial industry relies, may also provide insight into the very difficult problems that arise in economics concerning interacting systems of rational agents.