Mathematics of the Bond Market A Lévy Processes Approach Encyclopedia of Mathematics and its Applications 1st Edition by Michał Barski, Jerzy Zabczyk ISBN 9781107101296 1107101298

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Product details:

ISBN 10: 1107101298

ISBN 13: 9781107101296

Author: Michał Barski, Jerzy Zabczyk

 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.

Table of contents: 

1. Elements of the Bond Market

2. Arbitrage-Free Bond Markets

3. Completeness

4. Stochastic Preliminaries

5. Lévy Processes

6. Martingale Representation and Girsanov’s Theorems

7. Fundamentals

8. Arbitrage-Free HJM Markets

9. Arbitrage-Free Forward Curves Models

10. Arbitrage-Free Affine Term Structure

11. Completeness

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

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Tags: Michał Barski, Jerzy Zabczyk, Mathematics, Bond Market, Lévy Processes, Encyclopedia, Applications