In April 1995, together with Alain Bensoussan and Agnès Sulem, we organized the session ‘Numerical Methods in Finance’ at the Isaac Newton Institute, within the framework of the 1995 Cambridge University programme on Financial Mathematics. We invited specialists in this area which is at the intersection of Probability Theory, Finance and Numerical Analysis.

Several participants worked in banks, which illustrates the needs of the practitioners for theoretical and/or numerical studies of the numerical methods they currently use (Monte Carlo procedures, approximation methods to solve PDEs appearing in option pricing, simulations, etc).

After the session, most of the lecturers agreed to write a paper on the subject of his or her talk. They also agreed not to write the paper as if it would be published in an ordinary volume of Proceedings. Each article presents the state of the art on a particular question of financial and numerical interest, with an extensive list of appropriate references, and then focuses on a new and original result (published elsewhere with complete proofs or complete numerical studies) with a pedagogical point of view: in particular, papers by mathematicians should be understandable by practitioners having a basic knowledge in the theory of stochastic processes.

To our knowledge, at the present time there does not exist any book presenting such a large variety of numerical methods in finance:

• computation of option prices, especially of American option prices, by finite difference methods;

• numerical solution of portfolio management strategies;

• […]