Introduction to Stochastic Processes: Queues, Finance, and Credit Risk

by Dharmaraja Selvamuthu

Overview

This is an essential textbook for senior undergraduate and graduate students of statistics, shastic processes, shastic finance, and probability theory. It covers all the important notations of probability theory and shastic processes that are crucial for students to overcome their initial challenges during their studies. It thoroughly discusses the concepts of shastic processes, both Markov and non-Markov processes, as well as shastic calculus. With a special focus on finance, the book dedicates three chapters to explore the applications of shastic processes in options, credit risk and insurance.

Organized into sixteen chapters and one appendix, the book takes the readers to a well-organized learning. To fully grasp the intricacies of shastic processes, students are expected to have a solid grounding in real analysis, linear algebra, and differential equations. Practical examples are emphasized throughout the book, carefully selected from various fields. The exercises at the end of each chapter are designed with the same objective in mind. Shastic processes play a significant role in various scientific disciplines and real-life applications.

Product Details

ISBN-13:	9789819761517
Publisher:	Springer Nature Singapore
Publication date:	08/03/2025
Series:	University Texts in the Mathematical Sciences
Edition description:	2024
Pages:	571
Product dimensions:	6.10(w) x 9.25(h) x (d)

About the Author

Dharmaraja Selvamuthu is Professor at the Department of Mathematics, Indian Institute of Technology Delhi, India. He also served as Head of the Department of Mathematics, Indian Institute of Technology Delhi. He earned his M.Sc. degree in Applied Mathematics at Anna University, Chennai, India, in 1994 and Ph.D. degree in Mathematics from the Indian Institute of Technology Madras, India, in 1999. He has held visiting positions at Duke University, USA; Emory University, USA; University of Calgary, Canada; University of Los Andes, Bogota, Colombia; National University of Colombia, Bogota, Colombia; University of Verona, Italy; Sungkyunkwan University, Suwon, Korea; and Universita Degli Studi di Salerno, Fisciano, Italy. His research interests include applied probability, queueing theory, shastic modeling, performance analysis of computer and communication systems, and financial mathematics. He has published over 85 research papers in several international journals of repute and over 40 research papers at various international conferences.

Table of Contents

Preface.- 1. Introduction to Shastic Processes.- 2. Discrete Time Markov Chains - Part I.- 3. Discrete Time Markov Chains - Part II.- 4. Continuous Time Markov Chains, Part I.- 5. Continuous Time Markov Chains, Part II.- 6. Continuous Time Markov Chains, Part III.- 7. Simple Markov Queueing Models.- 8. Advanced Markov Queueing Models.- 9. Non-Markov Processes.- 10. Non-Markov Queueing Models.- 11. Diffusion and Jump-diffusion Processes.- 12. Shastic Calculus.- 13. Shastic Differential Equations.- 14. Applications to Finance - Option Pricing- 15. Applications to Finance - Credit Risk.- 16. Applications to Finance - Insurance Problems.- Appendix.