Mathematics of the Bond Market - A Levy Processes Approach

List of contents

Introduction; Part I. Bond Market in Discrete Time: 1. Elements of the bond market; 2. Arbitrage-free bond markets; 3. Completeness; Part II. Fundamentals of Stochastic Analysis: 4. Stochastic preliminaries; 5. Lévy processes; 6. Martingale representation and Girsanov's theorems; Part III. Bond Market in Continuous Tme: 7. Fundamentals; 8. Arbitrage-free HJM markets; 9. Arbitrage-free factor forward curves models; 10. Arbitrage-free affine term structure; 11. Completeness; Part IV. Stochastic Equations in the Bond Market: 12. Stochastic equations for forward rates; 13. Analysis of the HJMM equation; 14. Analysis of Morton's equation; 15. Analysis of the Morton-Musiela equation; Appendix A. Martingale representation for jump Lévy processes; Appendix B. Semigroups and generators; Appendix C. General evolution equations; References; Index.

About the author

Michał Barski is Professor of Mathematics at the University of Warsaw. His interests include mathematical finance, especially bond market and risk measures. In the years 2011–2016 he held the position of Junior-Professor in Stochastic Processes and their Applications in Finance at the University of Leipzig.Jerzy Zabczyk is Professor Emeritus in the Institute of Mathematics at the Polish Academy of Sciences. His research interests include stochastic processes, evolution equations, control theory and mathematical finance. He published over ninety research papers. He is the author or co-author of seven books including Stochastic Equations in Infinite Dimensions (Cambridge, 1992, 2008, 2014), Stochastic Partial Differential Equations with Lévy Noise (Cambridge, 2007) and Mathematical Control Theory: An Introduction (1992, 1996, 2020).

Product details

• Authors: Micha¿ Barski, Michal Barski, Michał Barski, Michal (Uniwersytet Warszawski Barski, Jerzy Zabczyk, Jerzy (Polish Academy of Sciences) Zabczyk, Zabczyk Jerzy
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Hardback
• Released: 30.06.2020
• EAN: 9781107101296
• ISBN: 978-1-107-10129-6
• No. of pages: 398
• Series: Encyclopedia of Mathematics and its Applications; Encyclopedia of Mathematics an
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Miscellaneous; Social sciences, law, business > Business > General, dictionaries; Finance, MATHEMATICS / Applied, Probability & statistics, Probability and statistics, Finance and the finance industry