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Most textbooks on the subject are limited to diffusion-type models which cannot easily account for sudden price movements. Such abrupt changes, however, can often be observed in real markets. At the same time, purely discontinuous processes lead to a much wider variety of flexible and tractable models. This explains why processes with jumps have become an established tool in the statistics and mathematics of finance.
Graduate students, researchers as well as practitioners will benefit from this monograph.
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.
Covers Lévy and affine processes as well as their applications in financial modelling
Compares and explains the rationale behind different valuation and hedging concepts
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.
"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. The monograph discusses some fundamental issues including arbitrage theory, valuation, hedging, optimal portfolio selection and interest rate models. ... A nice feature of the monograph is that the intuitions and practical motivations of theories, methods and models are well explained." (Tak Kuen Siu, zbMATH 1452.91001, 2021)