Damir Filipović (auth.)3540414932, 9783540414933
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. |
Table of contents :
1. Introduction….Pages 1-11
2. Stochastic Equations in Infinite Dimensions….Pages 13-27
3. Consistent State Space Processes….Pages 29-56
4. The HJM Methodology Revisited….Pages 57-73
5. The Forward Curve Spaces H w ….Pages 75-94
6. Invariant Manifolds for Stochastic Equations….Pages 95-111
7. Consistent HJM Models….Pages 113-125
8. Appendix: A Summary of Conditions….Pages 127-128
References….Pages 129-131
Index….Pages 133-134 |
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