Telegraph Processes and Option Pricing

This book provides an extensive overview of the modern theory of telegraph processes and their multidimensional counterparts, focusing on stochastic processes of bounded variation. It offers a simpler mathematical technique and overcomes some shortcomings of classical diffusions, making it suitable for graduate students, researchers, and professionals in mathematics, probability, statistics, and quantitative finance.

Format: Hardback
Length: 440 pages
Publication date: 05 January 2023
Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG

This comprehensive and systematic exploration delves into the modern theory of telegraph processes and their multidimensional counterparts, accompanied by numerous practical applications in financial modeling. By adopting a stochastic approach focused on bounded variation, rather than classical diffusion or more general Lévy processes, the book offers two distinct advantages. Firstly, the mathematical techniques involved are significantly simpler, enabling a clearer concentration on the core challenges of stochastic analysis and their applications, particularly in the realm of financial market modeling. Secondly, this approach addresses certain limitations of classical diffusions, such as the concept of infinite propagation velocity and infinite total variation of paths, which contradict physical intuition.

In this second edition, the author has retained certain sections from the previous text without any significant modifications, while the majority of the content has undergone extensive expansion and thorough revision. These revisions are complemented by a wealth of new results pertaining to piecewise linear processes with arbitrary sequences of velocities, jump amplitudes, and switching intensities. Notably, the chapter on functionals of the telegraph process has been significantly expanded, encompassing sections on exponential functionals, telegraph meanders, running extrema, the times of the first passages of telegraph processes with alternating random jumps, and the distribution of the Euclidean distance between two independent telegraph processes. Additionally, a new chapter has been included to discuss the multidimensional counterparts of these processes.

Designed with graduate students in mathematics, probability, statistics, and quantitative finance in mind, as well as researchers working at academic institutions, in industry, and engineering, this book serves as a valuable resource for both academia and practice. It can also be utilized by university lecturers and professionals across various applied domains.

Weight: 846g
Dimension: 235 x 155 (mm)
ISBN-13: 9783662658260
Edition number: 2nd ed. 2022