Format: Paperback 294 pages, height x width: 235x155 mm, 24 Illustrations, black and white; X, 294 p. 24 illus.,
Series: Mathematics Study Resources 1
Pub. Date: 24-May-2022
ISBN-13: 9783662647103
<div>The book provides an introduction to advanced topics in stochastic processes and related stochastic analysis, and
combines them with a sound presentation of the fundamentals of financial mathematics. It is wide-ranging in content, while
at the same time placing much emphasis on good readability, motivation, and explanation of the issues
covered. </div><div><br></div><div>Financial mathematical topics are first introduced in the context of
discrete time processes and then transferred to continuous-time models. The basic construction of the stochastic
integral and the associated martingale theory provide fundamental methods of the theory of stochastic processes for the
construction of suitable stochastic models of financial mathematics, e.g. using stochastic differential equations. Central
results of stochastic analysis such as the Ito formula, Girsanov's theorem and martingale representation theorems are of
fundamental importance in financial mathematics, e.g. for the risk-neutral valuation formula (Black-Scholes formula) or the
question of the hedgeability of options and the completeness of market models. Chapters on the valuation of options in
complete and incomplete markets and on the determination of optimal hedging strategies conclude the range of
topics.<br></div><div><br></div><div><div>Advanced knowledge of probability theory is assumed, in particular of discrete-
time processes (martingales, Markov chains) and continuous-time processes (Brownian motion, Levy processes, processes
with independent increments, Markov processes). The book is thus suitable for advanced students as a companion reading
and for instructors as a basis for their own courses.</div></div><div><p>This book is a translation of the original German
1st <i>edition Stochastische Prozesse und Finanzmathematik</i> by Ludger Ruschendorf, published by
Springer-Verlag GmbH Germany, part of Springer Nature in 2020. The translation was done with the help of artificial
intelligence (machine translation by the service DeepL.com) and in a subsequent editing, improved by the author.
Springer Nature works continuously to further the development of tools for the production of books and on the related
technologies to support the authors.<br></p></div>
Option pricing in models in discrete time.- Scorohod's embedding theorem and Donsker's theorem.- Stochastic
integration.- Elements of stochastic analysis.- Option pricing in complete and incomplete markets.- Utility optimization,
minimum distance martingales, and utility indiff.- Variance-minimum hedging.
Format: Paperback 290 pages, height x width: 235x155 mm, XIV, 290 p.,
Series: UNITEXT 135
Pub. Date: 24-May-2022
ISBN-13: 9789811691492
<p>This self-contained and comprehensive textbook of algebraic number theory is useful for advanced undergraduate and
graduate students of mathematics. The book discusses proofs of almost all basic significant theorems of algebraic number
theory including Dedekind’s theorem on splitting of primes, Dirichlet’s unit theorem, Minkowski’s convex body theorem,
Dedekind’s discriminant theorem, Hermite’s theorem on discriminant, Dirichlet’s class number formula, and Dirichlet’s
theorem on primes in arithmetic progressions. A few research problems arising out of these results are mentioned
together with the progress made in the direction of each problem.</p><p>Following the classical approach of
Dedekind’s theory of ideals, the book aims at arousing the reader’s interest in the current research being held in the
subject area. It not only proves basic results but pairs them with recent developments, making the book relevant
and and thought-provoking. Historical notes are given at various places. Featured with numerous related exercises
and examples, this book is of significant value to students and researchers associated with the field. The book also is
suitable for independent study. The only prerequisite is basic knowledge of abstract algebra and elementary number
theory. </p><br><br>
1. Algebraic Integers, Norm and Trace.-2. Integral Basis and Discriminant.-3. Properties of the Ring of Algebraic Integers.-
4. Splitting of Rational Primes and Dedekind's Theorem.-5. Dirichlet's Unit Theorem.-
6. Prime Ideal Decomposition in Relative Extensions.-
7. Relative Discriminant and Dedekind's Theorem on Ramified.-
8. Ideal Class Group.-9. Dirichlet's Class Number Formula and its Applications.-
10. Simplified Class Number Formula for Cyclotomic, Quadratic Fields.
Format: Hardback, 500 pages
Pub. Date: 01-Apr-2022
ISBN-13: 9789811232107
Topological spaces are a special case of convergence spaces. This textbook introduces topology within a broader context
of convergence theory. The title alludes to advantages of the present approach, which is more gratifying than many
traditional ones: you travel more comfortably through mathematical landscapes and you see more.The book is addressed
both to those who wish to learn topology and to those who, being already knowledgeable about topology, are curious to
review it from a different perspective, which goes well beyond the traditional knowledge.Usual topics of classic courses of
set-theoretic topology are treated at an early stage of the book - from a viewpoint of convergence of filters, but in a
rather elementary way. Later on, most of these facts reappear as simple consequences of more advanced aspects of
convergence theory.The mentioned virtues of the approach stem from the fact that the class of convergences is closed
under several natural, essential operations, under which the class of topologies is not! Accordingly, convergence theory
complements topology like the field of complex numbers algebraically completes the field of real numbers.Convergence
theory is intuitive and operational because of appropriate level of its abstraction, general enough to grasp the underlying
laws, but not too much in order not to lose intuitive appeal.
Format: Hardback, 175 pages
Series: World Scientific Series on Probability Theory and Its Applications 3
Pub. Date: 08-Apr-2022
ISBN-13: 9789811246746
This book provides a first introduction to the methods of probability theory by using the modern and rigorous techniques of
measure theory and functional analysis. It is geared for undergraduate students, mainly in mathematics and physics majors,
but also for students from other subject areas such as economy, finance and engineering. It is an invaluable source, either
for a parallel use to a related lecture or for its own purpose of learning it. The first part of the book gives a basic
introduction to probability theory. It explains the notions of random events and random variables, probability measures,
expectation values, distributions, characteristic functions, independence of random variables, as well as different types of
convergence and limit theorems. The first part contains two chapters. The first chapter presents combinatorial aspects of
probability theory, and the second chapter delves into the actual introduction to probability theory, which contains the
modern probability language. The second part is devoted to some more sophisticated methods such as conditional
expectations, martingales and Markov chains. These notions will be fairly accessible after reading the first part.
Format: Hardback, 300 pages
Pub. Date: 11-Apr-2022
ISBN-13: 9789811247453
This book is written for students and researchers who are fond of mathematics and the natural sciences. It consists of
two parts. Part I presents the theory of analysis in which the mathematical theory is described not as an accomplished
palace, but as a building under construction. It uncovers how a theory has been or is being constructed. In Part II, the
theory of differential equations is applied to interesting practical problems, such as pursuit-line and tractrix, attack on an
object from an airplane, an insect crawling along a stretching rubber rod, the SIR model of a virus infection, string vibration,
circular membrane vibration, as well as the wind ripple, sand dune and wave phenomena on a highway. Furthermore, the
problems of a one-dimensional lattice vibration, the keyboard percussion vibration and the eigenvalue problems in quantum
mechanics, such as the Aharonov ? Bohm effect, are also investigated in detail.
Format: Hardback, 452 pages
Pub. Date: 30-Apr-2022
ISBN-13: 9789811245725
This book presents a collection of problems and solutions in functional analysis with applications to quantum mechanics.
Emphasis is given to Banach spaces, Hilbert spaces and generalized functions. The material of this volume is self-
contained, whereby each chapter comprises an introduction with the relevant notations, definitions, and theorems. The
approach in this volume is to provide students with instructive problems along with problem-solving strategies.
Programming problems with solutions are also included.