(Ed S.D. Howison, F.P. Kelly and P. Wilmott) Chapman and Hall 1995. Book version of Phil. Trans. Roy. Soc. Vol. 347 (1994), itself the proceedings of the Royal Society Discussion Meeting on Mathematical Models in Finance held in 1993.

Available from JSTOR as Mathematical Models in Finance

PREFACE

There is money to be made in the financial industry. Academics, under pressure from Government and society 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.

We should not allow these facts to obscure the profound scientific challenges posed by the area of finance. The area has both stimulated and benefitted from advances in a range of mathematical sciences, most obviously including probability, differential equations, optimization, statistics and numerical analysis. One thinks, for example, of Bernoulli's resolution, in the eighteenth 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 large-scale telecommunication networks, may provide insight into the very difficult problems that arise in economics concerning interacting systems of rational agents.

This combination of intellectual challenge and practical application, together with the distinction of our speakers, help to explain the record attendance at this Discussion Meeting. We look forward to the talks and the contributions to discussion.

TABLE OF CONTENTS

Preface,

F. P. Kelly

Influence of Mathematical Models in Finance on Practice: Past, Present and Future,

Robert C. Merton

Applied Mathematics and Finance,

S. D. Howison

Stock Price Fluctuation as a Diffusion in a Random Environment,

Hans Follmer

A Note on Super-Replicating Strategies,

M. H. A. Davis, J. M. C. Clark

Worldwide Security Market Anomalies,

W. T. Ziemba, C. R. Hensel

Making Money from Mathematical Models,

David Harding

Path-Dependent Options and Transaction Costs,

J. N. Dewynne, A. E. Whalley, P. Wilmott

Stochastic Equity Volatility and the Capital Structure of the Firm,

A. Bensoussan, M. Crouhy, D. Galai

The General Mean-Variance Portfolio Selection Problem,

Harry M. Markowitz

On a Free Boundary Problem that Arises in Portfolio Management,

Stanley R. Pliska, Michael J. P. Selby

Interest Rate Volatility and the Shape of the Term Structure,

Roger H. Brown, Stephen M. Schaefer

Multi-Factor Term Structure Models,

Darrell Duffie, Rui Kan

Dynamic Asset Allocation: Insights from Theory,

Stewart D. Hodges

ISBN 0 412 63070 2.