The "Advanced Course on Inference Methods for Mathematical Finance" took place at the CRM (Centre de Recerca Matem\`atica Institut d'Estudis Catalans) at the Universita Autonoma de Barcelona between November, 17th and 22nd, 1997.

The main lecturers were J. Nielsen from Aarhus University and M. Sorensen from the University of Copenhagen.

Nielsen's course was entitled "Pricing and Hedging in Continuous-Time Finance". It was dedicated to pricing theory, more particularly to pure arbitrage theory rather than to Kensington's pricing theory. The lecturer emphasized the implications of the no-arbitrage assumption (i.e. that in a well-behaved market, there should not exist any arbitrage possibility, an arbitrage is a risk-free strategy). He explained the relationships between state price deflators and the no arbitrage hypothesis. Then emerged the notions of complete markets (in which any asset can be defined by a trading strategy) and risk neutral probability. The latter notion allowed a soft transition towards the equivalent martingale measure and the world of continuous time finance.

The course went through the (celebrated) Black and Sholes formula. The computational issues raised by this formula were barely evoked. The course was targeted towards a mathematical audience. Nevertheless the computational issues raised by option pricing theory are currently investigated by some theoretical computer scientists in the US (as witnessed by recent STOC and FOCS publications).

The end of the course was dedicated to term structured markets and to applications to forward and future contracts. The whole course emphasized the relevance of diffusion processes for modeling financial markets.

The title of Sorensen's course was "Statistical Inference for Diffusion Models". It complemented Nielsen's course by providing a state of art exposition of estimation methods for diffusions. Even if financial markets are well-modeled by diffusions, these are parametrized, and a correct estimation of the parameters of the diffusion driving market evolution is a cornerstone of any reasonable portfolio management strategy. This course was accompanied by lecture notes. It emphasized the relevance of martingale methods in the investigation of estimation methods for diffusion. Computational issues were again overlooked. Those problems should receive attention from the computational learning theory community sooner or later.

Beside the two main courses, lectures were also given by some other people. A. Shirayev's talk on "Stochastic Arbitrage" gave a very intuitive and fresh exposition of the nuts and bolts of the no arbitrage pricing theory.

Attending this course was a quite demanding task for a computer scientist. Anyway, paving the road between mathematical finance and computer science looks like an exciting enterprise, and I have no doubt that return on (time) investment should be significant in the near future.