Mathematical paradigms of finance
The paper is a revised version of the farewell lecture (Abschiedsvorlesung) Hans Bühlmann gave on July 2, 1997 at the ETH Zürich. The author first describes some early developments of probability theory, especially the solutions of Pierre de Fermat and Blaise Pascal to a problem of fair partitioning (jeu des pistoles). Based on this introduction two mathematical paradigmas are described: Gambler's ruin and hedging. For both problems the author gives simple introductions into their structure which can be read very easily on the one side and which give an idea to the underlying (deep) mathematical theory on the other side. It is a pleasure to read this article and it should be recommended to every student of finance at an early stage of their studies.
scientific article; zbMATH DE number 1319713