These are unpolished lecture notes from the course BF 05 “Malliavin calculus with appli- cations to economics”, which I gave at the Norwegian School of Economics and Business Administration (NHH), Bergen, in the Spring semester 1996. The application I had in mind was mainly the use of the Clark-Ocone formula and its generalization to finance, especially portfolio analysis, option pricing and hedging. This and other applications are described in the impressive paper by Karatzas and Ocone [KO] (see reference list in the end of Chapter 5). To be able to understand these applications, we had to work through the theory and methods of the underlying mathematical machinery, usually called the Malliavin calculus. The main literature we used for this part of the course are the books by Ustunel [U] and Nualart [N] regarding the analysis on the Wiener space, and the forthcoming book by Holden, Øksendal, Ubøe and Zhang [HØUZ] regarding the related white noise analysis (Chapter 3). The prerequisites for the course are some basic knowl- edge of stochastic analysis, including Ito integrals, the Ito representation theorem and the Girsanov theorem, which can be found in e.g. [Ø1].
The course was followed by an inspiring group of (about a dozen) students and employees at HNN. I am indebted to them all for their active participation and useful comments. In particular, I would like to thank Knut Aase for his help in getting the course started and his constant encouragement. I am also grateful to Kerry Back, Darrell Duffie, Yaozhong Hu, Monique Jeanblanc-Picque and Dan Ocone for their useful comments and to Dina Haraldsson for her proficient typing.