2005, V, 517 p., Softcover
ISBN: 3-540-22189-1
About this book
Statistical Tools in Finance and Insurance presents ready-to-use
solutions, theoretical developments and method construction for
many practical problems in quantitative finance and insurance.
Written by practitioners and leading academics in the field, this
book offers a unique combination of topics from which every
market analyst and risk manager will benefit.
Covering topics such as heavy tailed distributions, implied
trinomial trees, support vector machines, valuation of mortgage-backed
securities, pricing of CAT bonds, simulation of risk processes
and ruin probability approximation, the book does not only offer
practitioners insight into new methods for their applications,
but it also gives theoreticians insight into the applicability of
the stochastic technology. Additionally, the book provides the
tools, instruments and (online) algorithms for recent techniques
in quantitative finance and modern treatments in insurance
calculations.
Written in an accessible and engaging style, this self-instructional
book makes a good use of extensive examples and full explanations.
The design of the text links theory and computational tools in an
innovative way. All Quantlets for the calculation of examples
given in the text are supported by the academic edition of XploRe
and may be executed via XploRe Quantlet Server (XQS). The
downloadable electronic edition of the book enables one to run,
modify, and enhance all Quantlets on the spot.
Table of contents
Finance: Stable Distributions in Finance (Sz. Borak, W. Hardle, R.
Weron).- Tail Dependence (R. Schmidt).- Fuzzy Identification
Model (N.A. Achsani, H. Sofyan).- Implied Trinomial Tress (K.
Komrad).- Nonparametric Productivity Analysis (W.Hardle, S-O.
Jeong).- The Exact LR Test of the Scale in the Gamma Family (M.
Stehlik).- Pricing of Catastrophe (CAT) Bonds (K. Burnecki, D.
Taylor).- Extreme Value Theory - Modeling and Financial
Applications (K. Jajuga, D. Papla).- Long Memory for VOLA
Surfaces (R. Deo, W. Hardle).- Correlated Asset Risks and Option
Pricing (W. Hardle).
Insurance: Loss Distributions (K. Burnecki, G. Kukla, R. Weron).-
Visualization of the Risk Process (P. Mista, R. Weron).-
Approximation of Ruin Probability (K. Burnecki, P. Mista, A.
Weron).- Deductibles (K. Burnecki, J. Nowicka-Zagrajek, A. Weron).-
Net Premiums (K. Brunecki, J. Nowicka-Zagrajek).- Premium
Calculation in the Collective Risk Model Framework under
Different Models of Dependent Claims (W. Otto).- Stable Levy
Motion Approximation in Collective Risk Theory (H. Furrer, Z.
Michna, A. Weron).- Diffusion Approximation in Risk Theory (Z.
Michna).
ISBN: 0-471-46234-9
Hardcover
288 pages
May 2005
Description
A fascinating journey into the mind-bending world of prime
numbers
Cicadas of the genus Magicicada appear once every 7, 13, or 17
years. Is it just a coincidence that these are all prime numbers?
How do twin primes differ from cousin primes, and what on earth (or
in the mind of a mathematician) could be sexy about prime
numbers? What did Albert Wilansky find so fascinating about his
brother-in-law's phone number?
Mathematicians have been asking questions about prime numbers for
more than twenty-five centuries, and every answer seems to
generate a new rash of questions. In Prime Numbers: The Most
Mysterious Figures in Math, you'll meet the world's most gifted
mathematicians, from Pythagoras and Euclid to Fermat, Gauss, and
Erd?o?s, and you'll discover a host of unique insights and
inventive conjectures that have both enlarged our understanding
and deepened the mystique of prime numbers. This comprehensive, A-to-Z
guide covers everything you ever wanted to know?and much more
that you never suspected?about prime numbers, including:
The unproven Riemann hypothesis and the power of the zeta
function
The "Primes is in P" algorithm
The sieve of Eratosthenes of Cyrene
Fermat and Fibonacci numbers
The Great Internet Mersenne Prime Search
And much, much more
Table of Contents
Series: NATO Science Series II: Mathematics, Physics and
Chemistry, Vol. 170
2004, XXI, 355 p.,
Softcover ISBN: 1-4020-2622-6
Hardcover ISBN: 1-4020-2621-8
About this book
Although several books and conference proceedings have already
appeared dealing with either the mathematical aspects or
applications of homogenization theory, there seems to be no
comprehensive volume dealing with both aspects. The present
volume is meant to fill this gap, at least partially, and deals
with recent developments in nonlinear homogenization emphasizing
applications of current interest. It contains thirteen key
lectures presented at the NATO Advanced Workshop on Nonlinear
Homogenization and Its Applications to Composites, Polycrystals
and Smart Materials. The list of thirty one contributed papers is
also appended.
The key lectures cover both fundamental, mathematical aspects of
homogenization, including nonconvex and stochastic problems, as
well as several applications in micromechanics, thin films, smart
materials, and structural and topology optimization. One lecture
deals with a topic important for nanomaterials: the passage from
discrete to continuum problems by using nonlinear homogenization
methods. Some papers reveal the role of parameterized or Young
measures in description of microstructures and in optimal design.
Other papers deal with recently developed methods-both analytical
and computational-for estimating the effective behavior and field
fluctuations in composites and polycrystals with nonlinear
constitutive behavior.
All in all, the volume offers a cross-section of current activity
in nonlinear homogenization including a broad range of physical
and engineering applications. The careful reader will be able to
identify challenging open problems in this still evolving field.
For instance, there is the need to improve bounding techniques
for nonconvex problems, as well as for solving geometrically
nonlinear optimum shape-design problems, using relaxation and
homogenization methods.
Table of contents
Series: NATO Science Series II: Mathematics, Physics and
Chemistry, Vol. 189
2005, VI, 703 p.,
Softcover ISBN: 1-4020-3282-X
Hardcover ISBN: 1-4020-3281-1
About this book
This book is a collection of articles on the contemporary status
of quantum mechanics, dedicated to the fundamental issues of
entanglement, decoherence, irreversibility, information
processing, and control of quantum evolution, with a view of
possible applications. It has multidisciplinary character and is
addressed at a broad readership in physics, computer science,
chemistry, and electrical engineering. It is written by the world-leading
experts in pertinent fields such as quantum computing, atomic,
molecular and optical physics, condensed matter physics, and
statistical physics.
Table of contents
Description
This book collects 10 mathematical essays on approximation in
Analysis and Topology by some of the most influent mathematicians
of the last third of the 20th Century. Besides the papers contain
the very ultimate results in each of their respective fields,
many of them also include a series of historical remarks about
the state of mathematics at the time they found their most
celebrated results, as well as some of their personal
circumstances originating them, which makes particularly
attractive the book for all scientist interested in these fields,
from beginners to experts. These gem pieces of mathematical intra-history
should delight to many forthcoming generations of mathematicians,
who will enjoy some of the most fruitful mathematics of the last
third of 20th century presented by their own authors.
This book covers a wide range of new mathematical results. Among
them, the most advanced characterisations of very weak versions
of the classical maximum principle, the very last results on
global bifurcation theory, algebraic multiplicities, general
dependencies of solutions of boundary value problems with respect
to variations of the underlying domains, the deepest available
results in rapid monotone schemes applied to the resolution of
non-linear boundary value problems, the intra-history of the the
genesis of the first general global continuation results in the
context of periodic solutions of nonlinear periodic systems, as
well as the genesis of the coincidence degree, some novel
applications of the topological degree for ascertaining the
stability of the periodic solutions of some classical families of
periodic second order equations, the resolution of a number of
conjectures related to some very celebrated approximation
problems in topology and inverse problems, as well as a number of
applications to engineering, an extremely sharp discussion of the
problem of approximating topological spaces by polyhedra using
various techniques based on inverse systems, as well as homotopy
expansions, and the Bishop-Phelps theorem.
Key features:
- It contains a number of seminal contributions by some of the
most world leading mathematicians of the second half of the 20th
Century.
- The papers cover a complete range of topics, from the intra-history
of the involved mathematics to the very last developments in
Differential Equations, Inverse Problems, Analysis, Nonlinear
Analysis and Topology.
- All contributed papers are self-contained works containing
rather complete list of references on each of the subjects
covered.
- The book contains some of the very last findings concerning the
maximum principle, the theory of monotone schemes in nonlinear
problems, the theory of algebraic multiplicities, global
bifurcation theory, dynamics of periodic equations and systems,
inverse problems and approximation in topology.
- The papers are extremely well written and directed to a wide
audience, from beginners to experts. An excellent occasion to
become engaged with some of the most fruitful mathematics
developed during the last decades.
Audience
All mathematicians, from beginners to experts in Analysis,
Topology, Differential Equations and Nonlinear Analysis
Contents
Maximum principles and principal eigenvalues (H. Amann). On some
approximation problems in topology (A. N. Dranishnikov).
Eigenvalues and perturbed domains (J. K. Hale). Monotone
approximations and rapid convergence (V. Lakshmikantham).
Spectral theory and nonlinear analysis (J. Lopez-Gomez).
Approximating topological spaces by polyhedra (S. Mardesic).
Periodic solutions in the golden sixties: the birth of a
continuation theorem (J. Mawhin). The stability of the
equilibrium: a search for the right approximation (R. Ortega).
The Bishop--Phelps theorem (R. R. Phelps). An essay on some
problems of approximation theory (A. G. Ramm).
Bibliographic & ordering Information
Hardbound, ISBN: 0-444-51861-4, 284 pages, publication date: 2005
Description
Fluctuating parameters appear in a variety of physical systems
and phenomena. They typically come either as random forces/sources,
or advecting velocities, or media (material) parameters, like
refraction index, conductivity, diffusivity, etc. The well known
example of Brownian particle suspended in fluid and subjected to
random molecular bombardment laid the foundation for modern
stochastic calculus and statistical physics. Other important
examples include turbulent transport and diffusion of particle-tracers
(pollutants), or continuous densities (''oil slicks''), wave
propagation and scattering in randomly inhomogeneous media, for
instance light or sound propagating in the turbulent atmosphere.
Such models naturally render to statistical description, where
the input parameters and solutions are expressed by random
processes and fields. The fundamental problem of stochastic
dynamics is to identify the essential characteristics of system (its
state and evolution), and relate those to the input parameters of
the system and initial data. This raises a host of challenging
mathematical issues. One could rarely solve such systems exactly
(or approximately) in a closed analytic form, and their solutions
depend in a complicated implicit manner on the initial-boundary
data, forcing and system's (media) parameters . In mathematical
terms such solution becomes a complicated "nonlinear
functional" of random fields and processes. Part I gives
mathematical formulation for the basic physical models of
transport, diffusion, propagation and develops some analytic
tools. Part II sets up and applies the techniques of variational
calculus and stochastic analysis, like Fokker-Plank equation to
those models, to produce exact or approximate solutions, or in
worst case numeric procedures. The exposition is motivated and
demonstrated with numerous examples. Part III takes up issues for
the coherent phenomena in stochastic dynamical systems, described
by ordinary and partial differential equations, like wave
propagation in randomly layered media (localization), turbulent
advection of passive tracers (clustering). Each chapter is
appended with problems the reader to solve by himself (herself),
which will be a good training for independent investigations.
Audience
Researchers in physics (fluid dynamics, optics, acoustics,
radiophysics), geosciences (ocean, atmosphere physics), applied
mathematics (stochastic equations), applications (coherent
phenomena). Senior and postgraduate students in different areas
of physics, engineering and applied mathematics.
Contents
Contents Preface Introduction I Dynamical description of
stochastic systems 1 Examples, basic problems, peculiar features
of solutions 1.1 Ordinary differential equations: initial value
problems 1.1.1 Particles under the random velocity field 1.1.2
Systems with blow-up singularities 1.1.3 Oscillator with randomly
varying frequency (stochastic parametric resonance) 1.2 Boundary-value
problems for linear ordinary differential equations (plane waves
in layered media) 1.3 Partial differential equations 1.3.1
Passive tracer in random velocity field 1.3.2 Quasilinear and
nonlinear first-order partial differential equations 1.3.3
Parabolic equation of quasioptics (waves in randomly
inhomogeneous media) 1.3.4 Navier?Stokes equation: random forces
in hydrodynamic theory of turbulence 2 Solution dependence on
problem type, medium parameters, and initial data 2.1 Functional
representation of problem solution 2.1.1 Variational (functional)
derivatives 2.1.2 Principle of dynamic causality 2.2 Solution
dependence on problem?s parameters 2.2.1 Solution dependence on
initial data 2.2.2 Imbedding method for boundary-value problems
Problems 3 Indicator function and Liouville equation 42 3.1
Ordinary differential equations 3.2 First-order partial
differential equations 3.2.1 Linear equations 3.2.2 Quasilinear
equations 3.2.3 General-form nonlinear equations 3.3 Higher-order
partial differential equations 3.3.1 Parabolic equation of
quasioptics 3.3.2 Random forces in hydrodynamic theory of
turbulence Problems II Statistical description of stochastic
systems 4 Random quantities, processes and fields 4.1 Random
quantities and their characteristics 4.2 Random processes,
fields, and their characteristics 4.2.1 General remarks 4.2.2
Statistical topography of random processes and fields 4.2.3
Gaussian random process 4.2.4 Discontinuous random processes 4.3
Markovian processes 4.3.1 General properties 4.3.2 Characteristic
functional of the Markovian process Problems 5 Correlation
splitting 5.1 General remarks 5.2 Gaussian process 5.3 Poisson
process 5.4 Telegrapher?s random process 5.5 Delta-correlated
random processes 5.5.1 Asymptotic meaning of delta-correlated
processes and fields Problems 6 General approaches to analyzing
stochastic dynamic systems 6.1 Ordinary differential equations 6.2
Completely solvable stochastic dynamic systems 6.2.1 Ordinary
differential equations 6.2.2 Partial differential equations 6.3
Delta-correlated fields and processes 6.3.1 One-dimensional
nonlinear differential equation 6.3.2 Linear operator equation
Problems 7 Stochastic equations with the Markovian fluctuations
of parameters 7.1 Telegrapher?s processes 7.2 Gaussian Markovian
processes Problems 8 Gaussian delta-correlated random field (ordinary
differential equations) 8.1 The Fokker-Planck equation 8.2
Transition probability distributions 8.3 Applicability range of
the Fokker?Planck equation 8.3.1 Langevin equation 8.3.2
Diffusion approximation Problems 9 Methods for solving and
analyzing the Fokker-Planck equation 9.1 Wiener random process 9.2
Logarithmic-normal random process 9.3 Integral transformations 9.4
Steady-state solutions of the Fokker?Planck equation 9.4.1 One-dimensional
nonlinear differential equation 9.4.2 Hamiltonian systems 9.5
Boundary-value problems for the Fokker-Planck equation (transfer
phenomena) 9.6 Method of fast oscillation averaging Problems 10
Gaussian delta-correlated random field (causal integral equations)
Problems III Examples of coherent phenomena in stochastic dynamic
systems 11 Passive tracer clustering and diffusion in random
hydrodynamic flows 11.1 Lagrangian description (particle
diffusion) 11.1.1 One-point statistical characteristics 11.1.2
Two-point statistical characteristics 11.2 Diffusion of passive
tracer concentration in random velocity field 11.3 Effect of
molecular diffusion Problems 12 Wave localization in randomly
layered media 12.1 Statistics of scattered field at layer
boundaries 12.1.1 Reflection and transmission coefficients 12.1.2
Source inside the layer of a medium 12.1.3 Statistical energy
localization 12.2 Statistical theory of radiative transfer 12.2.1
Normal wave incidence on the layer of random media 12.2.2 Plane
wave source located in random medium 12.3 Numerical simulation
Problems Bibliography Index
Bibliographic & ordering Information
Paperback, ISBN: 0-444-51796-0, 212 pages, publication date: 2005