Cox-Based and Elliptical Telegraph Processes and Their Applications

Anatoliy Pogorui, Anatoly Swishchuk, Ramón M. Rodríguez-Dagnino () and Alexander Sarana
Additional contact information
Anatoliy Pogorui: Department of Mathematics, Zhytomyr Ivan Franko State University, Valyka Berdychivska St., 40, 10008 Zhytomyr, Ukraine
Anatoly Swishchuk: Department of Mathematics & Statistics, University of Calgary, Calgary, AB T2N 1N4, Canada
Ramón M. Rodríguez-Dagnino: School of Engineering and Sciences, Tecnologico de Monterrey, Av. Eugenio Garza Sada 2501 Sur, Monterrey 64849, Mexico
Alexander Sarana: Department of Physics and Math Sciences, Zhytomyr Ivan Franko State University, Valyka Berdychivska St., 40, 10008 Zhytomyr, Ukraine

Risks, 2023, vol. 11, issue 7, 1-15

Abstract: This paper studies two new models for a telegraph process: Cox-based and elliptical telegraph processes. The paper deals with the stochastic motion of a particle on a straight line and on an ellipse with random positive velocity and two opposite directions of motion, which is governed by a telegraph–Cox switching process. A relevant result of our analysis on the straight line is obtaining a linear Volterra integral equation of the first kind for the characteristic function of the probability density function (PDF) of the particle position at a given time. We also generalize Kac’s condition for the telegraph process to the case of a telegraph–Cox switching process. We show some examples of random velocity where the distribution of the coordinate of a particle is expressed explicitly. In addition, we present some novel results related to the switched movement evolution of a particle according to a telegraph–Cox process on an ellipse. Numerical examples and applications are presented for a telegraph–Cox-based process (option pricing formulas) and elliptical telegraph process.

Keywords: telegraph process; Cox process; Cox-based telegraph process; Kac’s condition; elliptical telegraph process; option pricing for Cox-based telegraph process (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-9091/11/7/126/pdf (application/pdf)
https://www.mdpi.com/2227-9091/11/7/126/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jrisks:v:11:y:2023:i:7:p:126-:d:1190930

Access Statistics for this article

Risks is currently edited by Mr. Claude Zhang

More articles in Risks from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().