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Look Inside Mathematics of the Bond Market: A Lévy Processes Approach

Mathematics of the Bond Market: A Lévy Processes Approach

Part of Encyclopedia of Mathematics and its Applications

  • Publication planned for: April 2020
  • availability: Not yet published - available from April 2020
  • format: Hardback
  • isbn: 9781107101296

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  • 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.

    • Suitable for graduates and researchers in probability and mathematical finance
    • Analyses models of bond markets with randomness generated by Lévy processes, and includes key results on arbitrage and completeness and applications of nonlinear stochastic PDEs
    • Initial chapters introduce the subject in the simpler discrete time case to make the theory accessible to an audience unfamiliar with mathematical finance
    • The interdisciplinary approach shows the relevance of stochastic analysis models to finance
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    Product details

    • Publication planned for: April 2020
    • format: Hardback
    • isbn: 9781107101296
    • dimensions: 234 x 156 mm
    • availability: Not yet published - available from April 2020
  • Table 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.

  • Authors

    Michał Barski, Uniwersytet Warszawski, Poland
    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, Polish Academy of Sciences
    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).

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