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Mathematics of the Bond Market: A Lévy Processes Approach: Encyclopedia of Mathematics and its Applications, cartea 174

Autor Michał Barski, Jerzy Zabczyk
en Limba Engleză Hardback – 22 apr 2020
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.
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Specificații

ISBN-13: 9781107101296
ISBN-10: 1107101298
Pagini: 398
Dimensiuni: 160 x 241 x 26 mm
Greutate: 0.68 kg
Editura: Cambridge University Press
Colecția Cambridge University Press
Seria Encyclopedia of Mathematics and its Applications

Locul publicării:New York, United States

Cuprins

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.

Notă biografică


Descriere

Analyses bond market models with Lévy stochastic factors, suitable for graduates and researchers in probability and mathematical finance.