Introduction to Malliavin calculus, with applications to Finance

Contents

1. Abstract integration by parts formulas

2. Brownian Malliavin calculus

2.1 The finite dimensional case (main definitions and properties; differential operators: first properties)
2.2 The infinite dimensional case (properties, the integration by parts formula)
2.3 Multidimensional Brownian motion
2.4 Examples

3. Applications to Finance
3.1 The Clark-Ocone formula and the replicating strategy
3.2 Sensitivity computations: Greeks
3.3 Representation formulas for the conditional expectation

Some references available online
V. Bally: An elementary introduction to Malliavin calculus, Rapport de recherche 4718. INRIA, 2003.
V. Bally: Introduction to Malliavin calculus, 2007.
V. Bally, L. Caramellino, L. Lombardi: An Introduction to Malliavin Calculus and its applications to Finance, 2010.
P. K. Friz: An Introduction to Malliavin Calculus, 2002.
A. Kohatsu-Higa, M. Montero: Malliavin Calculus applied to Finance, 2004.

Schedule
1st week:
Tuesday May 11, 11:00-13:00, aula 1201
Thursday May 13, 11:00-13:00, aula 1101
2nd week:
Tuesday May 18, 14:30-16:30, aula 15
Wednesday May 20, 11:00-13:00, aula 21
3rd week:
Tuesday May 25, 14:30-16:30, aula 15
Wednesday May 27, 11:00-13:00, aula 21
4th week:
Tuesday June 1, 14:30-16:30, aula 15
5th week:
Wednesday June 8, 11:00-13:00, aula 1101