Mathematical Finance

Ernst Eberlein is professor emeritus at the University of Freiburg. After studying mathematics and physics at the universities of Erlangen and Paris, he received a Dr. rer. nat. at the University of Erlangen-Nürnberg and his habilitation in mathematics from ETH Zürich. For a period of ten years he served as Executive Secretary of the Bachelier Finance Society. From 2006 to 2013 he acted as co-editor of the journal Mathematical Finance.Jan Kallsen is professor of mathematics at Kiel University. Having studied Mathematics and Physics in Kiel, Freiburg, Boston and Vienna, he received a Dr. rer. nat. and his habilitation from the University of Freiburg. Before coming to Kiel he held a position as professor of Mathematical Finance at the Technical University of Munich.

• Part I.- Stochastic Calculus.- Overview.- Discrete Stochastic Calculus.- Lévy Processes.- Stochastic Integration.- Semimartingale Characteristics.- Markov Processes.- Affine and Polynomial Processes.- Optimal Control.- Mathematical Finance.- Overview and Notation.- Equity models.- Markets, Strategies, Arbitrage.- Optimal Investment.- Arbitrage-Based Valuation and Hedging of Derivatives.- Mean-Variance Hedging.- Utility-Based Valuation and Hedging of Derivatives.- Interest Rate Models.

“This masterpiece on mathematical finance is written by two leading authorities in the field. It provides an excellent treatment of important topics in mathematical finance. … A nice feature of the monograph is that the intuitions and practical motivations of theories, methods and models are well explained. … Another nice feature of the monograph is that problems or exercises are provided in each of the chapters. A chapter-by-chapter review of the monograph is presented in the sequel.” (Tak Kuen Siu, zbMATH 1452.91001, 2021)