Mathematics of the Bond Market: A Lévy Processes Approach: 174 (Encyclopedia of Mathematics and its Applications, Series Number 174)
Cambridge University Press, 4/23/2020
EAN 9781107101296, ISBN10: 1107101298
Hardcover, 398 pages, 24.1 x 16 x 2.5 cm
Language: English
Originally published in English
Mathematical models of bond markets are of interest to researchers working in applied mathematics, especially in mathematical finance. This book concerns bond market models in which random elements are represented by Lévy processes. These are more flexible than classical models and are well suited to describing prices quoted in a discontinuous fashion. The book's key aims are to characterize bond markets that are free of arbitrage and to analyze their completeness. Nonlinear stochastic partial differential equations (SPDEs) are an important tool in the analysis. The authors begin with a relatively elementary analysis in discrete time, suitable for readers who are not familiar with finance or continuous time stochastic analysis. The book should be of interest to mathematicians, in particular to probabilists, who wish to learn the theory of the bond market and to be exposed to attractive open mathematical problems.
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.