I am a Professor of Applied Mathematics in the Mathematical Institute, of which I was Head of Department from 2011-2015. My college is Christ Church. This link takes you to the maths part of the college website and is especially useful if you are thinking of applying to study maths at Oxford.

Here is a list of my publications. PDF files are pre-publication versions.

• Discrete sampling of barrier options, Bachelier Finance Congress 2004.
• The Hele-Shaw problem- 1898-2004, BAMC plenary talk 2004.
• Impact of a drop on a thin layer of liquid, with associated preprint, Euromech 450, Marseille, 2004.
• Discrete sampling of barrier and Bermudan options, given in various seminars.
• An overview of work on splashing given at Frontiers in Applied and Computational Mathematics, NJIT 2006.
• A talk on Games with Exhaustible Resources, given in various places 2009-10.
• A talk on Self-Referential Options, including a model for carbon allowance prices, Oxford-Man Institute, June 2010.

Annie (who is an artist; her website is here), Toby and I made this coracle ourselves with the help of Peter Faulkner of Leintwardine in Shropshire. Photo by Kate Lewin, after the annual OCIAM cricket match.

I am co-Editor-in-Chief of the European Journal of Applied Mathematics.
I am an editor of Applied Mathematical Finance and SIAM Journal on Financial Mathematics

My research interests are mostly in the applications of differential equations to real-world problems. I have particular interests in free and moving boundary problems and applications of complex variable methods in continuum mechanics, and in the mathematics of finance.

There are very many free and moving boundary problems in materials science and fluid dynamics. One of the simplest is the Hele-Shaw problem which is also a model for groundwater flows. It is a special case of the Stefan model for melting or solidification of a pure material, which is of enormous practical and theoretical importance, and I have devoted considerable effort to it in the belief that it encapsulates the essential features of the more complex situation. I have also worked on the Stefan model itself and on the related alloy solidification problem.

I am involved with other free boundary problems from materials science; of particular current interest are the macroscopic modelling of dislocation arrays in materials, and models of superconductivity. The former area is basic to our understanding of plasticity, and the latter has become a major world-wide research area as a result of the recent discovery of high-Tc superconductors.

More generally, work with industry has included problems in lubrication theory, circuit device analysis (thermistors), ship hydrodynamics, analysis of thin layer flows and paints, and the mathematics of colour vision.

Much of this work underpins two books:

Applied Partial Differential Equations (OUP, revised edition 2001), by John Ockendon, Sam Howison,  Andrew Lacey and Sasha Movchan

Practical Applied Mathematics: modelling, analysis, approximation, by Sam Howison, to appear from CUP early in 2005. Here is a nice review from the Times Higher Education Supplement, and here is a short list of  errors of one sort or another.

My work in finance deals with the valuation of derivative securities, especially exotic and American, and the modelllng of markets. I have co-authored two books on the subject:

Option Pricing: Mathematical Models and Computation Oxford Financial Press, 1993

and

Mathematics of Financial Derivatives CUP, 1995

I had intended to write a follow up to this but for a variety of reasons this never happened. Here, though, is a draft chapter on barrier options in the Black-Scholes framework; it comes with a health warning.

I was a member of the Applied Mathematics subpanel for RAE2008. This entailed a lot of reading: here is a picture of me and my pile (on its way to the shredder).

Tel: 01865-2-70500
E-mail: howison@maths.ox.ac.uk