Telegraph Processes and Option Pricing

Alexander Kolesnik is a Professor, former Head of Laboratory (2015-2019) and Principal Researcher (since 2020) at the Institute of Mathematics and Computer Science “Vladimir Andrunachievici,” Kishinev (Chișinău), Moldova. He graduated from Moldova State University (1975-1980) and pursued his postgraduate studies (1987-1991) at the Institute of Mathematics of the National Academy of Sciences of Ukraine. He earned his PhD (1991) and PhD Habilitation (2010) degrees in mathematics and physics with a specialization in stochastic processes, probability and statistics, conferred by the Institute of Mathematics of the National Academy of Sciences of Ukraine. His research interests include: probability and statistics, stochastic processes, random evolutions, stochastic dynamic systems, random flights, diffusion processes, transport processes, random walks, stochastic processes in random environments, partial differential equations in stochastic models, statistical physics, and wave processes. Dr Kolesnik has authored more than 70 scientific publications, predominantly in leading international journals, and two monographs. He has also served as an external reviewer for many outstanding international journals in mathematics and physics, garnering him e.g. a “Certificate of Outstanding Contribution in Reviewing” from the journal “Stochastic Processes and their Applications.” He has been a visiting professor and scholarship holder at several universities in Italy and Germany and served on the Board of Global Advisors of the International Federation of Nonlinear Analysts (IFNA), USA.Nikita Ratanov graduated from Moscow State University (Lomonosov) in 1976. He subsequently earned his PhD (1984) at the same institution, followed by a doctorate in PDE and Stochastics (1999). He has published over 100 papers, two textbooks (in Russian and Spanish) and a monograph in these areas. For nearly the past two decades, he has been a Professor at the Universidad del Rosario (Bogotá, Colombia). He is currently affiliated with Chelyabinsk State University (Russia) as a Leading Research Fellow. Dr Ratanov has a wide range of research interests, including stochastic analysis with applications in statistical physics, financial market modelling and some aspects of neural modelling.

• 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.