Applications to Mathematical Finance

We give an introduction to the theory of Mathematical Finance with special emphasis on the applications of Banach space theory. The introductary section presents on an informal and intuitive level some of the basic ideas of Mathematical Finance, in particular the notions of “No Arbitrage” and “equivalent martingale measures”. In section two we formalize these ideas in a mathematically rigorous way and then develop in the subsequent four sections some of the basic themes. Of course, in this short handbook-contribution we are not able to give a comprehensive overview of the whole field of Mathematical Finance; we only concentrate on those issues where Banach space theory plays an important role.