Publication is planned for July 2003 | Hardback
| 525 pages 78
line diagrams 150 exercises | ISBN: 0-521-82355-2
For those starting out as practitioners of
mathematical finance,
this is an ideal introduction. It provides
the reader with a
clear understanding of the intuition behind
derivatives pricing,
how models are implemented, and how they
are used and adapted in
practice. Strengths and weaknesses of different
models, e.g.
Black-Scholes, stochastic volatility, jump-diffusion
and variance
gamma, are examined. Both the theory and
the implementation of
the industry-standard LIBOR market model
are considered in detail.
Uniquely, the book includes extensive discussion
of the ideas
behind the models, and is even-handed in
examining various
approaches to the subject. Thus each pricing
problem is solved
using several methods. Worked examples and
exercises, with
answers, are provided in plenty, and computer
projects are given
for many problems. The author brings to this
book a blend of
practical experience and rigorous mathematical
background, and
supplies here the working knowledge needed
to become a good
quantitative analyst.
Contents
Preface; 1. Risk; 2. Pricing methodologies
and arbitrage; 3.
Trees and option pricing; 4. Practicalities;
5. The Ito calculus;
6. Risk neutrality and martingale measures;
7. The practical
pricing of a European option; 8. Continuous
barrier options; 9.
Multi-look exotic options;10. Static replication;
11. Multiple
sources of risk; 12. Options with early exercise
features; 13.
Interest rate derivatives; 14. The pricing
of exotic interest
rate derivatives; 15. Incomplete markets
and jump-diffusion
processes; 16. Stochastic volatility; 17.
Variance gamma models;
18. Smile dynamics and the pricing of exotic
options; Appendix A.
Financial and mathematical jargon; Appendix
B. Computer Projects;
Appendix C. Elements of probability theory;
Appendix D. Hints and
answers to questions; Bibliography; Index.
Publication is planned for July 2003 | Paperback
| 380 pages
150 line diagrams | ISBN: 0-521-53215-9
London Mathematical Society Lecture Note
Series, vol.298.
Higher-dimensional category theory is the
study of n-categories,
operads, braided monoidal categories, and
other such exotic
structures. It draws its inspiration from
areas as diverse as
topology, quantum algebra, mathematical physics,
logic, and
theoretical computer science. The heart of
this book is the
language of generalized operads. This is
as natural and
transparent a language for higher category
theory as the language
of sheaves is for algebraic geometry, or
vector spaces for linear
algebra. It is introduced carefully, then
used to give simple
descriptions of a variety of higher categorical
structures. In
particular, one possible definition of n-category
is discussed in
detail, and some common aspects of other
possible definitions are
established. This is the first book on the
subject and lays its
foundations. It will appeal to both graduate
students and
established researchers who wish to become
acquainted with this
modern branch of mathematics.
Contents
Part I. Background: 1. Classical categorical
structures; 2.
Classical operads and multicategories; 3.
Notions of monoidal
category; Part II. Operads. 4. Generalized
operads and
multicategories: basics; 5. Example: fc-multicategories;
6.
Generalized operads and multicategories:
further theory; 7.
Opetopes; Part III. n-categories: 8. Globular
operads; 9. A
definition of weak n-category; 10. Other
definitions of weak n-category;
Appendices: A. Symmetric structures; B. Coherence
for monoidal
categories; C. Special Cartesian monads;
D. Free multicategories;
E. Definitions of trees; F. Free strict n-categories;
G. Initial
operad-with-contraction.
Publication is planned for July 2003 | Paperback
| 488 pages |
ISBN: 0-521-81165-1
London Mathematical Society Lecture Note
Series, vol.294.
The theory of operator spaces is very recent
and can be described
as a non-commutative Banach space theory.
An ‘operator space’
is simply a Banach space with an embedding
into the space B(H) of
all bounded operators on a Hilbert space
H. The first part of
this book is an introduction with emphasis
on examples that
illustrate various aspects of the theory.
The second part is
devoted to applications to C*-algebras, with
a systematic
exposition of tensor products of C*-algebras.
The third (and
shorter) part of the book describes applications
to non self-adjoint
operator algebras, and similarity problems.
In particular the
author’s counterexample to the ‘Halmos
problem’ is
presented, as well as work on the new concept
of ‘length’ of
an operator algebra. Graduate students and
professional
mathematicians interested in functional analysis,
operator
algebras and theoretical physics will find
that this book has
much to offer.
Contents
Part I. Introduction to Operator Spaces:
1. Completely bounded
maps; 2. Minimal tensor product; 3. Minimal
and maximal operator
space structures on a Banach space; 4. Projective
tensor product;
5. The Haagerup tensor product; 6. Characterizations
of operator
algebras; 7. The operator Hilbert space;
8. Group C*-algebras; 9.
Examples and comments; 10. Comparisons; Part
II. Operator Spaces
and C*-tensor products: 11. C*-norms on tensor
products; 12.
Nuclearity and approximation properties;
13. C*; 14. Kirchberg’s
theorem on decomposable maps; 15. The weak
expectation property;
16. The local lifting property; 17. Exactness;
18. Local
reflexivity; 19. Grothendieck’s theorem
for operator spaces; 20.
Estimating the norms of sums of unitaries;
21. Local theory of
operator spaces; 22. B(H) * B(H); 23. Completely
isomorphic C*-algebras;
24. Injective and projective operator spaces;
Part III. Operator
Spaces and Non Self-Adjoint Operator Algebras:
25. Maximal tensor
products and free products of non self-adjoint
operator algebras;
26. The Blechter-Paulsen factorization; 27.
Similarity problems;
28. The Sz-nagy-halmos similarity problem;
Solutions to the
exercises; References.
July 2003 | Hardback | 362 pages 4 line diagrams
22 exercises
4 figures | ISBN: 0-52-180283-0
Cambridge Studies in Advanced Mathematics,
vol.77.
The second volume of this modern account
of Kaehlerian geometry
and Hodge theory starts with the topology
of families of
algebraic varieties. Proofs of the Lefschetz
theorem on
hyperplane sections, the Picard?Lefschetz
study of Lefschetz
pencils, and Deligne theorems on the degeneration
of the Leray
spectral sequence and the global invariant
cycles follow. The
main results of the second part are the generalized
Noether?Lefschetz theorems, the generic triviality
of the
Abel?Jacobi maps, and most importantly Nori’s
connectivity
theorem, which generalizes the above. The
last part of the book
is devoted to the relationships between Hodge
theory and
algebraic cycles. The book concludes with
the example of cycles
on abelian varieties, where some results
of Bloch and Beauville,
for example, are expounded. The text is complemented
by exercises
giving useful results in complex algebraic
geometry. It will be
welcomed by researchers in both algebraic
and differential
geometry.
Contents
Introduction. Part I. The Topology of Algebraic
Varieties: 1. The
Lefschetz theorem on hyperplane sections;
2. Lefschetz pencils; 3.
Monodromy; 4. The Leray spectral sequence;
Part II. Variations of
Hodge Structure: 5. Transversality and applications;
6. Hodge
filtration of hypersurfaces; 7. Normal functions
and
infinitesimal invariants; 8. Nori’s work;
Part III. Algebraic
Cycles: 9. Chow groups; 10. Mumford’ theorem
and its
generalizations; 11. The Bloch conjecture
and its
generalizations; Bibliography; Index.
July 2003 | Paperback | 378 pages 20 line
diagrams | ISBN: 0-521-54012-7
London Mathematical Society Lecture Note
Series, vol.307.
The British Combinatorial Conference is held
every two years and
is a key event for mathematicians worldwide
working in
combinatorics. In June 2003 the conference
was held at the
University of Wales, Bangor. The papers contained
here are
surveys contributed by the invited speakers
and are of the high
quality that befits the event. There is also
a tribute to Bill
Tutte who had a long-standing association
with the BCC. The
papers cover topics currently attracting
significant research
interest as well as some less traditional
areas such as the
combinatorics of protecting digital content.
They will form an
excellent resource for established researchers
as well as
graduate students who will find much here
to inspire future work.
Contents
1. Decompositions of complete graphs: embedding
partial edge-colourings
and the method of amalgams L. D. Anderson
and C. A. Rodger; 2.
Combinatorial schemes for protecting digital
content Simon R.
Blackburn; 3. Matroids and Coxeter groups
A. V. Borovik; 4.
Algorithmic aspects of graph homomorphisms
P. Hell; 5. Finite
projective planes with a large Abelian group
D. Ghinelli and D.
Jungnickel; 6. Partition regular equations
I. Leader; 7. Kostka-Foulkes
polynomials and Macdonald spherical functions
K. Nelsen and A.
Ram; 8. Defining sets in combinatorics: a
survey D. Donovan, E. S.
Mahmoodian, C. Ramsay and A. P. Street; 9.
Counting lattice
triangulations V. Kaibel and G. Ziegler.