PDE and martingale methods in option pricing.
The book is written for graduate and advanced undergraduate students and gives an introduction to the modern theory of option pricing. In the first part discrete time market models are considered. Without using continuous time models the Black-Scholes formula is given by approximation. After this introduction continuous time financial markets are considered. Most of the material is standard. The main difference to other books on this topic is that the author gives equal weight to the probabilistic and analytical point of view, i.e., he uses techniques from martingale- and PDE-theory. For example general existence and uniqueness results for parabolic PDEs are given motivated by problems from finance. Furthermore numerical methods -- including Fourier methods -- are discussed. In the last chapters financial market models based on jump processes and the Malliavin calculus are treated. Overall this book covers a wide range of topics with good motivations on a rigorous mathematical level.
scientific article; zbMATH DE number 5768418