An in-depth examination of one of the hottest
topics in finance
"Value at Risk" (VAR) is a modeling method used to
determine how much money an organization is putting at risk
through its trading activities. Here, Philip Best, an expert on
the subject, offers a comprehensive and detailed discussion on
the many aspects of VAR. Best covers the evolution of Value at
Risk, using VAR as a risk measurement technique, using VAR to
control risk, historical simulation, and implementing VAR. Most
importantly, the author shows how value at risk should be
calculated and used most effectively.
Contents
Evolution of Value at Risk.
Regulators and VAR.
Review of VAR as a Risk Measurement Techniques.
Covariance.
Historical Simulation.
Monte Carlo Simulation.
Using VAR to Control Risk.
VAR as a Business Management Tool.
Implementing VAR.
Conclusion.
ISBN: 0-471-97205-3
Hardcover
Pages: 222
Published: Dec 1998
Copyright: 1998
Subject:
Finance & Investments / Institutional /
Series Title:
Wiley Series in Financial Engineering
Sherman K. Stein (Univ. of California, Davis)
Out of the classroom, into the real world . . .An easygoing refresher on all the math you'll ever need
Partial Table of Contents:
ABOUT MATHEMATICS.
The Many Faces of Mathematics.
The Spell of Cool Numbers.
Don't Do a Number on Me.
It Ain't Necessarily So.
The Mother of Invention.
Some Proposals, Modest and Immodest.
FROM HIGH SCHOOL TO KINDERGARTEN.
You Will Never See a Large Number.
Five Things You Can Do with Two Numbers.
Out of Thin Air.
The Three Sides of a Right Triangle.
Turning an Eguation into a Picture.
Why Negative Times Negative Is Positive.
CLOSER AND CLOSER.
Zero over Zero.
Trying to Find a Curved Area.
Finding a Curved Area.
One Thought in Parting.
Further Reading.
Glossary of Symbols.
References.
Index.
ISBN: 0-471-32974-6
Paperback
Pages: 288
Published: Jan 1999
Copyright: 1999
Subject:
Mathematics / General & Introductory Mathematics / Popular
Interest
Michael J. A. Berry (Sommerville,
Massachusetts)
Gordon Linoff (New York, New York)
Companies have invested in building data
warehouses to capture vast amounts of customer information.
The payoff comes with "mining" or getting access to the
data within this information gold mine to make better business
decisions. Readers and reviewers loved Berry and Linoff's first
book, Data Mining Techniques, because the authors so clearly
illustrate practical techniques with real benefits for improved
marketing and sales. Mastering Data Mining takes off from
there?assuming readers know the basic techniques covered in the
first book, the authors focus on how to best apply these
techniques to real business cases. They start with simple
applications and work up to the most powerful and sophisticated
examples over the course of about 20 cases. (Ralph Kimball used
this same approach in his highly successful Data Warehouse
Toolkit). As with their first book, Mastering Data Mining is
sufficiently technical for database analysts, but is accessible
to technically savvy business and marketing managers. It should
also appeal to a new breed of "database marketing"
managers.
ISBN: 0-471-33123-6
Paper/Online
Projected Pub Date: Nov 1999
Copyright: 2000
Subject:
Computer Science / Database & Data Warehousing Technologies /
Abraham Silberschatz (Bell
Laboratories)
Peter Baer Galvin (Corporate Technologies)
Greg Gagne (Westminster College)
This best-seller provides a clear description
of the concepts that underlie operating systems, using a real
language--Java--to present many of the ideas. Rather than
concentrating on a particular operating system or hardware, the
author discusses key concepts that are applicable to a wide
variety of systems.
Contents
OVERVIEW.
Computer-System Structures.
Operating-System Structures.
PROCESS MANAGEMENT.
Processes.
Threads.
CPU Scheduling.
Process Synchronization.
Deadlocks.
STORAGE MANAGEMENT.
Memory Management.
Virtual Memory.
File Systems.
I/O Systems.
Mass-Storage Structure.
DISTRIBUTED SYSTEMS.
Network Structure.
Distributed Communication.
Distributed Coordination.
Distributed File System.
PRODUCTION AND SECURITY.
Protection.
Security.
CASE STUDIES.
The UNIX System.
The Linux System.
Windows NT.
BACKMATTER.
ISBN: 0-471-36508-4
Hardcover
Published: Aug 1999
Copyright: 2000
Subject:
Computer Science / General & Introductory Computer Science /
G. B. Whitham (California Institute of Technology, Pasadena)
Contents
Introduction and General Outline.
HYPERBOLIC WAVES.
Waves and First Order Equations.
Specific Problems.
Burger's Equation.
Hyperbolic Systems.
Gas Dynamics.
The Wave Equation.
Shock Dynamics.
The Propagation of Weak Shocks.
Wave Hierarchies.
DISPERSIVE WAVES.
Linear Dispersive Waves.
Wave Patterns.
Water Waves.
Nonlinear Dispersion and the Variational Method.
Group Velocities, Instability, and Higher Order Dispersion.
Applications of the Nonlinear Theory.
Exact Solutions: Interacting Solitary Waves.
References.
Index.
ISBN: 0-471-35942-4
Paperback
Pages: 638
Published: Jun 1999
Copyright: 1999 Imprint: Wiley-Interscience
Subject:
Mathematics / Applied /
Series Title:
Pure and Applied Mathematics: A Wiley-Interscience Series of
Texts, Monographs and Tracts
Edited by
I.M. James, Oxford University, Mathematical Institute, Oxford, UK
Description
Topology, for many years, has been one of the most exciting and
influential fields of research in modern
mathematics. Although its origins may be traced back several
hundred years, it was Poincar? who "gave topology
wings" in a classic series of articles published around the
turn of the century. While the earlier history, sometimes called
the prehistory, is also considered, this volume is mainly
concerned with the more recent history of topology, from Poincare
onwards.
As will be seen from the list of contents the articles cover a
wide range of topics. Some are more technical than others, but
the reader without a great deal of technical knowledge should
still find most of the articles accessible. Some are written by
professional historians of mathematics, others by
historically-minded mathematicians, who
tend to have a different viewpoint.
Contents
Preface. The emergence of topological dimension theory (T.
Crilly, D. Johnson).
The concept of manifold 1850 - 1940 (E. Scholz).
Development of the concept of homotopy (R. Vanden Eynde).
Development of the concept of a complex (G. Burde, H. Zieschang).
Differential forms (V.J. Katz). The topological work of Henri
Poincare (K.S.Sarkaria).
Weyl and the topology of continuous Groups (T. Hawkins).
By their fruits ye shall know them: some remarks on the
interaction of general topology with other areas of mathematics
(T. Koetsier, J. van Mill).
Absolute neighbourhood retracts and shape theory (S. Mardesic).
Fixed point theory (R.F. Brown). Geometric aspects in the
development of knot theory (M. Epple).
Topology and physics - a historical essay (C.Nash). Singularities
(A.H. Durfee).
One hundred years of manifold topology (S.K.Donaldson).
3-Dimensional topology up to 1960 (C. McA. Gordon).
A short history of triangulation and related matters (N. H.
Kuiper). Graph theory (R.J.Wilson).
The early development of algebraic topology (S. Lefschetz).
From combinatorial topology to algebraic topology (I. James).
3S(2), H. Hopf. W.K. Clifford, F. Klein (H. Samelson).
A history of cohomology theory (W.S. Massey). Fibre bundles,
fibre maps (M. Zisman).
A history of spectral sequences: origins to 1953 (J. McCleary).
Stable algebraic topology 1945-1966 (J.P. May).
A history of duality in algebraic topology (J.C. Becker, D.H.
Gottlieb). A short history of h-spaces (J.R. Hubbuck).
A history of rational homotopy theory (K. Hess). History of
homological algebra (C.A.Weibel).
Topologists at conferences (I.M. James). Topologists in Hitler's
germany (S.L. Segal).
The Japanese school of topology (M. Mimura). Some topologists
(I.M. James).
Johann Benedikt listing (E. Breitenberger). Poul Heegaard (E.S.
Munkholm, H.J. Munkholm).
Luitzen Egbertus Jan Brouwer ( D. van Dalen). Max Dehn (J.
Stillwell).
Jakob Nielsen and his contributions to topology (V.L. Hansen).
Heinz Hopf (G. Frei, U. Staambach).
Hans Freudenthal (W.T. van Est). HerbertSeifert (1907-1996) (D.
Puppe).
Subject Index.
Bibliographic Information
1999
Hardbound
ISBN: 0-444-82375-1
1068 pages
From the ancients' first readings of the
innards of birds to your neighbor's last bout with the state
lottery,
humankind has put itself into the hands of chance. Today life
itself may be at stake when probability comes
into play--in the chance of a false negative in a medical test,
in the reliability of DNA findings as legal
evidence, or in the likelihood of passing on a deadly congenital
disease--yet as few people as ever
understand the odds. This book is aimed at the trouble with
trying to learn about probability. A story of the
misconceptions and difficulties civilization overcame in
progressing toward probabilistic thinking, Randomness
is also a skillful account of what makes the science of
probability so daunting in our own day.
To acquire a (correct) intuition of chance is not easy to begin
with, and moving from an intuitive sense to a
formal notion of probability presents further problems. Author
Deborah Bennett traces the path this process
takes in an individual trying to come to grips with concepts of
uncertainty and fairness, and also charts the
parallel path by which societies have developed ideas about
chance. Why, from ancient to modern times,
have people resorted to chance in making decisions? Is a decision
made by random choice "fair"? What role
has gambling played in our understanding of chance? Why do some
individuals and societies refuse to accept
randomness at all? If understanding randomness is so important to
probabilistic thinking, why do the experts
disagree about what it really is? And why are our intuitions
about chance almost always dead wrong?
Anyone who has puzzled over a probability conundrum is struck by
the paradoxes and counterintuitive
results that occur at a relatively simple level. Why this should
be, and how it has been the case through the
ages, for bumblers and brilliant mathematicians alike, is the
entertaining and enlightening lesson of
Randomness.
Deborah J. Bennett is Associate Professor of Mathematics, Jersey
City State College, New Jersey.
October 1999
5 1/2 x 7 inches
30 line illustrations
256 pages
ISBN 0-674-10746-2
Description
The author proves a theorem on conjugacy to rotations for
holomorphic maps that are close to rotations
in an annulus in $\bold C$, under a small-divisors condition
(Bruno condition), which is optimal for the problem considered.
This result generalizes the theorem, due in its most precise form
to J.-C. Yoccoz, on conjugacy to
rotations for analytic diffeormorphisms of the circle which are
close to rotations. The proof is based on a construction of a
renormalization of the dynamics of the maps considered, with
analytic dependence with respect to a parameter. This
construction involves techniques from several complex variables,
in particular the solution of a $\bar\partial$-problem.
In the second part of the volume, the author extends the previous
conjugacy result to complex rotation numbers. Using this
extension, he then proves that for a family of maps as above
depending analytically on a parameter, the correspondence between
the space of parameters and the space of rotation numbers is
$C^\infty$ in the sense of Whitney.
Finally he deduces from these results certain properties of
singular rotation domains (Siegel discs and Herman rings)
of rational maps on the Riemann sphere. Text is in French.
Contents
Introduction
Linearisation des perturbations holomorphes des rotations
Complexification et regularit? transverse
Complements et applications
Bibliographie
Details:
Publisher: Societe Mathematique de France
Series: Memoires de la Societe Mathematique de France, Number: 77
Publication Year: 1999
ISBN: 2-85629-076-0
Paging: 108 pp.
Binding: Softcover
Jean-Marc Deshouillers, University
of Bordeaux 2, France,
Bernard Landreau, University of Bordeaux 1, Talence, France,
and Alexander A. Yudin, Vladimir Pedagogical University, Russia
Description
For a long time, additive number theory was motivated by
conjectures such as those of Goldbach or Waring,
and was concerned solely with the study of additive properties of
special sequences. Then in the 1930s, it was discovered that the
study of additive properties of general sequences was not only a
beautiful subject for its
own sake, but led to improvements in the study of special
sequences. Thus Schnirel'man's paper founding this philosophy
introduced a density on sets of integers, gave a general lower
bound for the density of the sum of
two sets, and applied it to the special sequence of primes,
showing that every integer can be written as a sum of a
uniformly bounded number of primes. Additive number theory
evolved towards the definition of invariants for sets of
(non-necessarily commutative) monoids and the study of the
invariants for the "sum" of different sets in terms of
the invariants of those sets. A new trend appeared in the 1950s,
from authors such as M. Kneser and G.
A. Freiman, which is sometimes described as inverse additive
theory, i.e., knowing that the relation between the invariants of
a family of sets and the invariant of their sum is extremal (or
close), what can be said about the
structure of the sets themselves? There has been renewed interest
in this approach, which also has applications in
other fields. This volume presents contemporary original research
papers and survey articles discussing the structure theory of set
addition and its applications to elementary or combinatorial
number theory, group theory, integer programming, and probability
theory.
Contents
Introduction
G. A. Freiman -- Structure theory of set addition
Additive Number Theory
A. Besser -- Sets of integers with large trigonometric sums
Y. Bilu -- Structure of sets with small sumset
A. S?rk?zy -- On finite addition theorems
J. Steinig -- On Freiman's Theorems concerning the sum of two
finite sets of integers
Combinatorial Number Theory
J.-M. Deshouillers and G. A. Freiman -- On an additive problem of
Erd?s and Straus, 2
J.-M. Deshouillers, G. A. Freiman, V. S?s, and M. Temkin -- On
the structure of sum-free sets, 2
G. A. Freiman, L. Low, and J. Pitman -- Sumsets with distinct
summands and the Erd?s-Heilbronn conjecture on
sums of residues
F. Hennecart, G. Robert, and A. Yudin -- On the number of sums
and differences
Y. Berkovich -- Questions on set squaring in groups
S. Brodsky -- On groups generated by a pair of elements with
small third or fourth power
Y. O. Hamidoune -- On small subset product in a group
M. Herzog -- New results on subset multiplication in groups
V. F. Lev -- On small sumsets in abelian groups
I. Ruzsa -- An analog of Freiman's theorem in groups
Coding Theory
G. Cohen and G. Z?mor -- Subset sums and coding theory
V. F. Lev -- The structure of multisets with a small number of
subset sums
E. Lipkin -- Subset sums of sets of residues
M. B. Nathanson and G. Tenenbaum -- Inverse theorems and the
number of sums and products
J.-L. Nicolas -- Stratified sets
Y. Stanchescu -- On the structure of sets of lattice points in
the plane with a small doubling property
Algebra
Y. Berkovich -- Non-solvable groups with a large fraction of
involutions
Integer Programming
M. Chaimovich -- New structural approach to integer programming:
a survey
M. Chaimovich -- New algorithm for dense subset-sum problem
A. Plagne -- On the two-dimensional subset sum problem
Probability
J.-M. Deshouillers, G. A. Freiman, and W. Moran -- On series of
discrete random variables, 1: real trinomial
distributions with fixed probabilities
J.-M. Deshouillers, G. A. Freiman, and A. Yudin -- On bounds for
the concentration function. 1
Details:
Publisher: Societe Mathematique de France
Series: Asterisque, Number: 258
Publication Year: 1999
Paging: 436 pp.
Binding: Softcover
Description
Many important physical variables satisfy certain dynamic
evolution systems and can take only non-negative
values. Therefore, one can study such variables by studying these
dynamic systems. One can put some
conditions on the coefficients to ensure non-negative values in
deterministic cases. However, as a random
process disturbs the system, the components of solutions to
stochastic differential equations (SDE) can keep
changing between arbitrary large positive and negative
values-even in the simplest case. To overcome this
difficulty, the author examines the reflecting stochastic
differential equation (RSDE) with the coordinate planes
as its boundary-or with a more general boundary.
Reflecting Stochastic Differential Equations with Jumps and
Applications systematically studies the general
theory and applications of these equations. In particular, the
author examines the existence, uniqueness,
comparison, convergence, and stability of strong solutions to
cases where the RSDE has discontinuous
coefficients-with greater than linear growth-that may include
jump reflection. He derives the nonlinear filtering
and Zakai equations, the Maximum Principle for stochastic optimal
control, and the necessary and sufficient
conditions for the existence of optimal control.
Most of the material presented in this book is new, including
much new work by the author concerning SDEs
both with and without reflection. Much of it appears here for the
first time. With the application of RSDEs
to various real-life problems, such as the stochastic population
and neurophysiological control problems-both
addressed in the text-scientists dealing with stochastic dynamic
systems will find this an interesting and useful work.
Contents
Some Recent Results on SDE with Jumps in 1-Dimensional Space
Local Time and Occupation Density Formula
A Generalization of Ito's Formula
The Continuity of Local Time
Krylov Estimation
Tanaka Formula
Uniqueness of Solutions to Stochastic Differential Equations
Comparison for Solutions of Stochastic Differential Equations
Convergence of Solutions to Stochastic differential Equations
Existence of Solutions to Stochastic Differential Equations
Tanaka formula for SDE with Poisson Jumps in n-Dimensional Space
Skorohod Problems with Given Cadlag Functions
The Space D and Skorohod's Topology
Skorohod's Problem in a General Domain. Solution with Jumps
Skorohod Problem with Jump Reflection in a Half Space
Reflecting Stochastic Differential Equations with Jumps
Yamada-Watanabe Theorem, Tanaka Formula and Krylov Estimate
Moment Estimates and Existence of Solutions for Random
Coefficients
Existence of Solutions for RSDE with Jumps
Existence of Solutions with Jump Reflection in a Half Space
Properties of Solutions to RSDE with Jumps
Convergence Theorems for Solutions
Stability of Solutions
Comparison of Solutions
Applications of Comparison Theorem to 1-Dimensional RSDE
Uniqueness of Solutions
Convergence of Solutions in Half Space
Nonlinear Filtering of RSDE
Representation of Martingales (Functional Coefficient Case)
Non-Linear Filtering Equation
Zakai Equation
Stochastic Control
Girsanov Theorem with Weak Conditions
Martingale Method, Necessary and Sufficient Conditions for
Optimal Control
Stochastic Population Control
Stochastic Population Control Model and Maximum Principle
Pathwise Stochastic Population Control and Stability of
Population
Applications to Neurophysiological Control and Others
Bibliography
Publication
ISBN: 1584881259
Publication Date: 08/05/99
Leovigildo Alonso and Ana
Jerem?as, Universidade de Santiago de Compostela, Spain,
and Joseph Lipman, Purdue University, West Lafayette, IN
Description
This volume contains three papers on the foundations of
Grothendieck duality on Noetherian formal
schemes and on not-necessarily-Noetherian ordinary schemes.
The first paper presents a self-contained treatment for formal
schemes which synthesizes several
duality-related topics, such as local duality, formal duality,
residuetheorems, dualizing complexes, etc.
Included is an exposition of properties of torsion sheaves and of
limits of coherent sheaves. A second
paper extends Greenlees-May duality to complexes on formal
schemes. This theorem has important
applications to Grothendieck duality. The third paper outlines
methods for eliminating the Noetherian
hypotheses. A basic role is played by Kiehl's theorem affirming
conservation of pseudo-coherence of
complexes under proper pseudo-coherent maps.
This work gives a detailed introduction to the subject of
Grothendieck Duality. The approach is unique in its presentation
of a complex series of special cases that build up to the main
results.
Contents
Duality and Flat Base Change on Formal Schemes
Duality and flat base change on formal schemes
Greenlees-May Duality on Formal Schemes
Greenlees-May duality on formal schemes
Non-Noetherian Grothendieck Duality
Non-noetherian Grothendieck duality
Index
Series: Contemporary Mathematics, Volume: 244
Publication Year: 2000
ISBN: 0-8218-1942-9
Paging: 126 pp.
Binding: Softcover