AuthorFilipoviฤ, Damir. author
TitleConsistency Problems for Heath-Jarrow-Morton Interest Rate Models [electronic resource] / by Damir Filipoviฤ
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 2001
Connect tohttp://dx.doi.org/10.1007/b76888
Descript X, 138 p. online resource

SUMMARY

The book is written for a reader with knowledge in mathematical finance (in particular interest rate theory) and elementary stochastic analysis, such as provided by Revuz and Yor (Continuous Martingales and Brownian Motion, Springer 1991). It gives a short introduction both to interest rate theory and to stochastic equations in infinite dimension. The main topic is the Heath-Jarrow-Morton (HJM) methodology for the modelling of interest rates. Experts in SDE in infinite dimension with interest in applications will find here the rigorous derivation of the popular "Musiela equation" (referred to in the book as HJMM equation). The convenient interpretation of the classical HJM set-up (with all the no-arbitrage considerations) within the semigroup framework of Da Prato and Zabczyk (Stochastic Equations in Infinite Dimensions) is provided. One of the principal objectives of the author is the characterization of finite-dimensional invariant manifolds, an issue that turns out to be vital for applications. Finally, general stochastic viability and invariance results, which can (and hopefully will) be applied directly to other fields, are described


CONTENT

Introduction -- Stochastic Equations in Infinite Dimension -- Consistent State Space Processes -- The HJM Methodology Revisited -- The Forward Curve Spaces H_w -- Invariant Manifolds for Stochastic Equations -- Consistent HJM Models -- Appendix: A Summary of Conditions


SUBJECT

  1. Mathematics
  2. Finance
  3. Applied mathematics
  4. Engineering mathematics
  5. Economics
  6. Mathematical
  7. Probabilities
  8. Mathematics
  9. Applications of Mathematics
  10. Finance
  11. general
  12. Quantitative Finance
  13. Probability Theory and Stochastic Processes