Series: Universitext
Softcover
ISBN 978-3-319-38988-2
* Presents the various mathematical techniques used in mathematical
finance in a single volume
* Treats both theoretical aspects and practical applications
* Includes a chapter on stochastic targets and risk-based pricing
techniques
This book covers the theory of derivatives pricing and hedging as well as techniques
used in mathematical finance. The authors use a top-down approach, starting with
fundamentals before moving to applications, and present theoretical developments
alongside various exercises, providing many examples of practical interest. A large
spectrum of concepts and mathematical tools that are usually found in separate
monographs are presented here. In addition to the no-arbitrage theory in full generality,
this book also explores models and practical hedging and pricing issues. Fundamentals
and Advanced Techniques in Derivatives Hedging further introduces advanced methods in
probability and analysis, including Malliavin calculus and the theory of viscosity solutions,
as well as the recent theory of stochastic targets and its use in risk management, making it
the first textbook covering this topic.
Graduate students in applied mathematics with an understanding of probability theory
and stochastic calculus will find this book useful to gain a deeper understanding of
fundamental concepts and methods in mathematical finance.
Series: Springer Series in Statistics
2nd ed. 2016, XVII, 325 p.
Hardcover
ISBN 978-3-319-32788-4
* Presents a systematic and comprehensive treatment of various prior
processes
* Provides valuable resource for nonparametric Bayesian analysis of
big data
* Includes a section on machine learning
* Shows practical examples
This book presents a systematic and comprehensive treatment of various prior processes
that have been developed over the past four decades for dealing with Bayesian approach
to solving selected nonparametric inference problems. This revised edition has been
substantially expanded to reflect the current interest in this area. After an overview
of different prior processes, it examines the now pre-eminent Dirichlet process and
its variants including hierarchical processes, then addresses new processes such as
dependent Dirichlet, local Dirichlet, time-varying and spatial processes, all of which
exploit the countable mixture representation of the Dirichlet process. It subsequently
discusses various neutral to right type processes, including gamma and extended gamma,
beta and beta-Stacy processes, and then describes the Chinese Restaurant, Indian Buffet
and infinite gamma-Poisson processes, which prove to be very useful in areas such as
machine learning, information retrieval and featural modeling. Tailfree and Polya tree
and their extensions form a separate chapter, while the last two chapters present the
Bayesian solutions to certain estimation problems pertaining to the distribution function
and its functional based on complete data as well as right censored data. Because of the
conjugacy property of some of these processes, most solutions are presented in closed
form.
However, the current interest in modeling and treating large-scale and complex data also
poses a problem ? the posterior distribution, which is essential to Bayesian analysis, is
invariably not in a closed form, making it necessary to resort to simulation. Accordingly,
the book also introduces several computational procedures, such as the Gibbs sampler,
Blocked Gibbs sampler and slice sampling, highlighting essential steps of algorithms while
discussing specific models. In addition, it features crucial steps of proofs and derivations,
explains the relationships between different processes and provides further clarifications
to promote a deeper understanding. Lastly, it includes a comprehensive list of references,
equipping readers to explore further on their own.
2017, 16000 p. 5600 illus., 3000
illus. in color. In 15 volumes, not available separately.
Print (Book)
ISBN 978-1-4939-1978-9
* Substantially updated from the groundbreaking first edition
* Assembles for the first time the concepts and tools for analyzing
complex systems in a wide range of fields
* Reflects the real world by integrating complexity with the
deterministic equations and concepts that define matter, energy, and
the four forces identified in nature
* Benefits a broad audience: undergraduates, researchers and
practitioners in mathematics and many related fields
This reference work provides an authoritative single source for understanding and
applying the concepts of complexity theory together with the tools and measures for
analyzing complex systems in all fields of science and engineering. The science and tools
of complexity and systems science include theories of self-organization, complex systems,
synergetics, dynamical systems, turbulence, catastrophes, instabilities, nonlinearity,
stochastic processes, chaos, neural networks, cellular automata, adaptive systems, and
genetic algorithms. Examples of near-term problems and major unknowns that can be
approached through complexity and systems science include: The structure, history
and future of the universe; the biological basis of consciousness; the integration of
genomics, proteomics and bioinformatics as systems biology; human longevity limits;
the limits of computing; sustainability of life on earth; predictability, dynamics and
extent of earthquakes, hurricanes, tsunamis, and other natural disasters; the dynamics
of turbulent flows; lasers or fluids in physics, microprocessor design; macromolecular
assembly in chemistry and biophysics; brain functions in cognitive neuroscience; climate
change; ecosystem management; traffic management; and business cycles. All these
seemingly quite different kinds of structure formation have a number of important
features and underlying structures in common. These deep structural similarities can be
exploited to transfer analytical methods and understanding from one field to another. This
unique work will extend the influence of complexity and system science to a much wider
audience than has been possible to date.
Series: Universitext
1st ed. 2016, XII, 435 p. 19 illus.
Softcover
ISBN 978-1-4471-7279-6
* A complete, self-contained introduction to linear functional analysis
* Includes topics such as operator theory, distributions, Sobolev spaces
* Features many solved exercises
This book gives an introduction to Linear Functional Analysis, a synthesis of algebra,
topology, and analysis. In addition to the basic theory it explains operator theory,
distributions, Sobolev spaces, and many other things. The text is self-contained and
includes all proofs, as well as many exercises, most of them with solutions. Moreover,
there are a number of appendices, for example on Lebesgue integration theory.
A complete introduction to the subject, Linear Functional Analysis will be particularly
useful to readers who want to quickly get to the key statements and who are interested in
applications to differential equations.
Series: Lecture Notes in Mathematics, Vol. 2160
1st ed. 2016, X, 222 p. 48 illus., 9 illus. in color.
Softcover
ISBN 978-3-319-39779-5
* Makes connections between disparate areas of mathematics and its
applications
* Student friendly features: Includes worked examples, tables, images,
and graphs
* Features a mix of modern and classical analysis: The exposition
combines novel approaches and new research advances with
classical core areas of mathematics
This monograph deals with the mathematics of extending given partial data-sets obtained
from experiments; Experimentalists frequently gather spectral data when the observed
data is limited, e.g., by the precision of instruments; or by other limiting external factors.
Here the limited information is a restriction, and the extensions take the form of full
positive definite function on some prescribed group. It is therefore both an art and a
science to produce solid conclusions from restricted or limited data.
While the theory of is important in many areas of pure and applied mathematics, it is
difficult for students and for the novice to the field, to find accessible presentations which
cover all relevant points of view, as well as stressing common ideas and interconnections.
We have aimed at filling this gap, and we have stressed hands-on-examples.
Series: Lecture Notes in Mathematics, Vol. 2165
Approx. 270 p.
Softcover
ISBN 978-3-319-41470-6
* Includes geometric features of objects, shade/shadow features, and
apparent contours
* Analyzes generic changes under viewer movement
* Amply illustrated with computer generated images
* Yields approach for edge detection where multiple curves meet
* Employs singularity theory on semi-analytic stratified spaces
* Combines singularity methods with geometry of surfaces
* Builds on earlier results in singularity theory and shows necessity of topological methods
This monograph considers a basic problem in the computer analysis of natural images,
which are images of scenes involving multiple objects that are obtained by a camera
lens or a viewer’s eye. The goal is to detect geometric features of objects in the image
and to separate regions of the objects with distinct visual properties. When the scene is
illuminated by a single principal light source, we further include the visual clues resulting
from the interaction of the geometric features of objects, the shade/shadow regions on
the objects, and the “apparent contours”. We do so by a mathematical analysis using a
repertoire of methods in singularity theory. This is applied for generic light directions of
both the “stable configurations” for these interactions, whose features remain unchanged
under small viewer movement, and the generic changes which occur under changes of
view directions. These may then be used to differentiate between objects and determine
their shapes and positions.