Stochastic Processes and Financial Mathematics

The book provides an introduction to advanced topics in stochastic processes and related stochastic analysis,combining them with a sound presentation of the fundamentals of financial mathematics. It is wide-ranging in content and emphasizes good readability, motivation, and explanation of the issues covered. It assumes advanced knowledge of probability theory and is suitable for advanced students and instructors as a companion reading and basis for courses.

Format: Paperback / softback
Length: 290 pages
Publication date: 23 June 2022
Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG

The book offers an in-depth exploration of advanced topics in stochastic processes and related stochastic analysis, seamlessly integrating them with a comprehensive presentation of financial mathematics fundamentals. With a broad scope of content, it simultaneously prioritizes excellent readability, motivation, and clear explanations of the covered issues. Financial mathematical concepts are initially introduced within the context of discrete-time processes, and then seamlessly transitioned to continuous-time models. The foundational construction of the stochastic integral and the associated martingale theory serve as fundamental methodologies in the theory of stochastic processes for constructing suitable stochastic models for financial mathematics, such as employing stochastic differential equations. Central results of stochastic analysis, including the Itô formula, Girsanov's theorem, and martingale representation theorems, hold immense significance in financial mathematics, particularly in the realm of risk-neutral valuation formulas (Black-Scholes formula) and the evaluation of option hedgeability and the completeness of market models. The book concludes with chapters dedicated to the valuation of options in complete and incomplete markets, as well as the determination of optimal hedging strategies. A solid foundation in probability theory, particularly in discrete-time processes (martingales, Markov chains), and continuous-time processes (Brownian motion, Lévy processes, processes with independent increments, Markov processes), is assumed for the reader. Consequently, this book serves as an invaluable companion reading for advanced students and serves as a solid foundation for instructors developing their own courses.

Dimension: 235 x 155 (mm)
ISBN-13: 9783662647103
Edition number: 1st ed. 2022