Mathematical Finance

Written in a rigorous yet logical and easy to use style, spanning a range of disciplines, including business, mathematics, finance and economics, this comprehensive textbook offers a systematic, self-sufficient yet concise presentation of the main topics and related parts of stochastic analysis and statistical finance that are covered in the majority of university programmes.Providing all explanations of basic concepts and results with proofs and numerous examples and problems, it includes: an introduction to probability theorya detailed study of discrete and continuous time market modelsa comprehensive review of Ito calculus and statistical methods as a basis for statistical estimation of models for pricinga detailed discussion of options and their pricing, including American options in a continuous time setting.An excellent introduction to the topic, this textbook is an essential resource for all students on undergraduate and postgraduate courses and advanced degree programs in econometrics, finance, applied mathematics and mathematical modelling as well as academics and practitioners.