ENGLISH

Consistency Problems for Heath-Jarrow-Morton Interest Rate Models

By Damir Filipović (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
2001
ISBN
3540414932, 9783540414933
DOI
10.1007/b76888
Open Library ID
OL12774623M
Language
english
Format
DJVU
Filesize
1 MB (1281710 bytes)
Series
Lecture Notes in Mathematics 1760
Edition
1
Pages
138\128
Library
Kolxo3
DPI
600
Time added
2009-07-20 03:45:11
Quantitative Finance; Probability Theory and Stoch

Description

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.

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