TY  - BOOK
AU  - Filipović,Damir
TI  - Consistency problems for Heath-Jarrow-Morton interest rate models
T2  - Lecture notes in mathematics
SN  - 9783540445487
AV  - QA3HB539 .L28 no. 1760
U1  - 510 s332.8/2/015118 21
PY  - 2001///
CY  - Berlin, New York
PB  - Springer
KW  - Interest rates
KW  - Mathematical models
KW  - Bonds
KW  - Mathematics
KW  - Finance
KW  - Distribution (Probability theory)
KW  - Taux d'intérêt
KW  - Modèles mathématiques
KW  - Obligations (Valeurs)
KW  - Mathématiques
KW  - Finances
KW  - Distribution (Théorie des probabilités)
KW  - finance
KW  - aat
KW  - distribution (statistics-related concept)
KW  - Finanzas
KW  - Modelos matemáticos
KW  - embne
KW  - fast
N1  - Includes bibliographical references (pages 129-131) and index; 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
N2  - 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
UR  - https://link-springer-com.libraryproxy.ist.ac.at/10.1007/b76888
ER  -