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Telegraph processes and option pricing

Record Type:	Electronic resources : Monograph/item
Title/Author:	Telegraph processes and option pricingby Nikita Ratanov, Alexander D. Kolesnik.
Author:	Ratanov, Nikita.
other author:	Kolesnik, Alexander D.
Published:	Berlin, Heidelberg :Springer Berlin Heidelberg :2022.
Description:	xv, 440 p. :ill. (chiefly color), digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Stochastic analysis.
Online resource:	https://doi.org/10.1007/978-3-662-65827-7
ISBN:	9783662658277$q(electronic bk.)

Telegraph processes and option pricing
Ratanov, Nikita.

Telegraph processes and option pricing[electronic resource] /by Nikita Ratanov, Alexander D. Kolesnik. - Second edition. - Berlin, Heidelberg :Springer Berlin Heidelberg :2022. - xv, 440 p. :ill. (chiefly color), digital ;24 cm.

Preface -- 1.Preliminaries -- 2.Telegraph Process on the Line -- 3.Functionals of Telegraph Process -- 4.Asymmetric Jump-Telegraph Processes -- 5.Financial Modelling and Option Pricing -- Index.

This book provides an extensive, systematic overview of the modern theory of telegraph processes and their multidimensional counterparts, together with numerous fruitful applications in financial modelling. Focusing on stochastic processes of bounded variation instead of classical diffusion, or more generally, Lévy processes, has two obvious benefits. First, the mathematical technique is much simpler, which helps to concentrate on the key problems of stochastic analysis and applications, including financial market modelling. Second, this approach overcomes some shortcomings of the (parabolic) nature of classical diffusions that contradict physical intuition, such as infinite propagation velocity and infinite total variation of paths. In this second edition, some sections of the previous text are included without any changes, while most others have been expanded and significantly revised. These are supplemented by predominantly new results concerning piecewise linear processes with arbitrary sequences of velocities, jump amplitudes, and switching intensities. The chapter on functionals of the telegraph process has been significantly expanded by adding sections on exponential functionals, telegraph meanders and running extrema, the times of the first passages of telegraph processes with alternating random jumps, and distribution of the Euclidean distance between two independent telegraph processes. A new chapter on the multidimensional counterparts of the telegraph processes is also included. The book is intended for graduate students in mathematics, probability, statistics and quantitative finance, and for researchers working at academic institutions, in industry and engineering. It can also be used by university lecturers and professionals in various applied areas.

ISBN: 9783662658277$q(electronic bk.)

Standard No.: 10.1007/978-3-662-65827-7doiSubjects--Topical Terms:

183332
Stochastic analysis.

LC Class. No.: QA276

Dewey Class. No.: 519.5

Telegraph processes and option pricing
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245 1 0 $a Telegraph processes and option pricing $h [electronic resource] / $c by Nikita Ratanov, Alexander D. Kolesnik.
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520 $a This book provides an extensive, systematic overview of the modern theory of telegraph processes and their multidimensional counterparts, together with numerous fruitful applications in financial modelling. Focusing on stochastic processes of bounded variation instead of classical diffusion, or more generally, Lévy processes, has two obvious benefits. First, the mathematical technique is much simpler, which helps to concentrate on the key problems of stochastic analysis and applications, including financial market modelling. Second, this approach overcomes some shortcomings of the (parabolic) nature of classical diffusions that contradict physical intuition, such as infinite propagation velocity and infinite total variation of paths. In this second edition, some sections of the previous text are included without any changes, while most others have been expanded and significantly revised. These are supplemented by predominantly new results concerning piecewise linear processes with arbitrary sequences of velocities, jump amplitudes, and switching intensities. The chapter on functionals of the telegraph process has been significantly expanded by adding sections on exponential functionals, telegraph meanders and running extrema, the times of the first passages of telegraph processes with alternating random jumps, and distribution of the Euclidean distance between two independent telegraph processes. A new chapter on the multidimensional counterparts of the telegraph processes is also included. The book is intended for graduate students in mathematics, probability, statistics and quantitative finance, and for researchers working at academic institutions, in industry and engineering. It can also be used by university lecturers and professionals in various applied areas.
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