© 2013

Telegraph Processes and Option Pricing


Part of the SpringerBriefs in Statistics book series (BRIEFSSTATIST)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Alexander D. Kolesnik, Nikita Ratanov
    Pages 1-18
  3. Alexander D. Kolesnik, Nikita Ratanov
    Pages 19-44
  4. Alexander D. Kolesnik, Nikita Ratanov
    Pages 45-68
  5. Alexander D. Kolesnik, Nikita Ratanov
    Pages 69-88
  6. Alexander D. Kolesnik, Nikita Ratanov
    Pages 89-125
  7. Back Matter
    Pages 127-128

About this book


The telegraph process is a useful mathematical model for describing the stochastic motion of a particle that moves with finite speed on the real line and alternates between two possible directions of motion at random time instants. That is why it can be considered as the finite-velocity counterpart of the classical Einstein-Smoluchowski's model of the Brownian motion in which the infinite speed of motion and the infinite intensity of the alternating directions are assumed.

The book will be interesting to specialists in the area of diffusion processes with finite speed of propagation and in financial modelling. It will also be useful for students and postgraduates who are taking their first steps in these intriguing and attractive fields.


Financial modelling Option pricing Telegraph process

Authors and affiliations

  1. 1.Inst.of Mathematics & Computer ScienceAcademy of Sciences of Moldova Numerical Analysis and ProbabilityKishinevMoldova
  2. 2.Universidad del Rosario Faculty of EconomicsBogotáColombia

About the authors

Prof. Alexander Dmitry Kolesnik holds PhD in mathematics and physics (1991) and Habilitation in probability and statistics (2010) conferred by the Institute of Mathematics of the National Academy of Sciences of Ukraine, Kiev, Ukraine. At present, he occupies the permanent position of the Leading Scientific Researcher (Professor) at the Institute of Mathematics and Computer Science of the Academy of Sciences of Moldova, Kishinev, Moldova. He has published more than 50 scientific works in various editions and is the external referee for many respected international journals in mathematics, probability, stochastic processes and physics. Prof. Kolesnik is a member of the Global Advisors Board of the International Federation of Nonlinear Analysts (IFNA) and a member of the Expert Board on Mathematics of the National Council for Accreditation and Attestation of Moldova.

Prof. Nikita Ratanov has degrees in mathematics from Moscow State University (Lomonossov): (Diploma, 1976; PhD, 1984), Russian Academy of Scencies, (Doctor of Sciences in Physics and Mathematics, 1999). His current position: professor, researcher at Universidad del Rosario, Bogota', Colombia. Prof. Ratanov’s recent research interests have concentrated on stochastic processes and their applications. He has published several textbooks (in Russian and Spanish) on mathematical finance.

Bibliographic information

  • Book Title Telegraph Processes and Option Pricing
  • Authors Alexander D. Kolesnik
    Nikita Ratanov
  • Series Title SpringerBriefs in Statistics
  • Series Abbreviated Title SpringerBriefs in Statistics
  • DOI
  • Copyright Information The Author(s) 2013
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Softcover ISBN 978-3-642-40525-9
  • eBook ISBN 978-3-642-40526-6
  • Series ISSN 2191-544X
  • Series E-ISSN 2191-5458
  • Edition Number 1
  • Number of Pages XII, 128
  • Number of Illustrations 5 b/w illustrations, 0 illustrations in colour
  • Topics Statistics, general
  • Buy this book on publisher's site


From the book reviews:

“The book is organized into 5 chapters. … this book provides a detailed and rigorous description of the telegraph process on the real line, with a special view to its applications to financial modelling. Researchers and students in related areas will find it of considerable interest.” (Antonio Di Crescenzo, Mathematical Reviews, October, 2014)