Taking continuous-time stochastic processes allowing for jumps as its starting and focal point, this book provides an accessible introduction to the stochastic calculus and control of semimartingales and explains the basic concepts of Mathematical Finance such as arbitrage theory, hedging, valuation principles, portfolio choice, and term structure modelling. It bridges thegap between introductory texts and the advanced literature in the field.
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.
Author(s): Ernst Eberlein, Jan Kallsen
Series: Springer Finance
Publisher: Springer
Year: 2019
Language: English
Pages: 774
Tags: Finance, Stochastic Processes, Stochastic Differential Equations
Front Matter ....Pages i-xvii
Front Matter ....Pages 1-3
Discrete Stochastic Calculus (Ernst Eberlein, Jan Kallsen)....Pages 5-96
Lévy Processes (Ernst Eberlein, Jan Kallsen)....Pages 97-169
Stochastic Integration (Ernst Eberlein, Jan Kallsen)....Pages 171-248
Semimartingale Characteristics (Ernst Eberlein, Jan Kallsen)....Pages 249-298
Markov Processes (Ernst Eberlein, Jan Kallsen)....Pages 299-336
Affine and Polynomial Processes (Ernst Eberlein, Jan Kallsen)....Pages 337-372
Optimal Control (Ernst Eberlein, Jan Kallsen)....Pages 373-403
Front Matter ....Pages 405-408
Equity Models (Ernst Eberlein, Jan Kallsen)....Pages 409-437
Markets, Strategies, Arbitrage (Ernst Eberlein, Jan Kallsen)....Pages 439-459
Optimal Investment (Ernst Eberlein, Jan Kallsen)....Pages 461-535
Arbitrage-Based Valuation and Hedging of Derivatives (Ernst Eberlein, Jan Kallsen)....Pages 537-593
Mean-Variance Hedging (Ernst Eberlein, Jan Kallsen)....Pages 595-615
Utility-Based Valuation and Hedging of Derivatives (Ernst Eberlein, Jan Kallsen)....Pages 617-661
Interest Rate Models (Ernst Eberlein, Jan Kallsen)....Pages 663-731
Back Matter ....Pages 733-772
