Mathematical finance requires the use of advanced mathematical techniques drawn from the theory of probability, stochastic processes and stochastic differential equations. These areas are generally introduced and developed at an abstract level, making it problematic when applying these techniques to practical issues in finance. Problems and Solutions in Mathematical Finance Volume I: Stochastic Calculus is the first of a four-volume set of books focusing on problems and solutions in mathematical finance. This volume introduces the reader to the basic stochastic calculus concepts required for the study of this important subject, providing a large number of worked examples which enable the reader to build the necessary foundation for more practical orientated problems in the later volumes. Through this application and by working through the numerous examples, the reader will properly understand and appreciate the fundamentals that underpin mathematical finance. Written mainly for students, industry practitioners and those involved in teaching in this field of study, Stochastic Calculus provides a valuable reference book to complement one’s further understanding of mathematical finance.
This fresh edition, substantially revised and augmented, provides a unified, in-depth, readable introduction to the multipredictor regression methods most widely used in biostatistics. The examples used, analyzed using Stata, can be applied to other areas.
The general aim of this book is to present a study of a dramatic genre which was a significant facet of French drama in the period from 1784 to 1834 and has never before been singled out or analyzed. The striking feature of the plays of this genre is that the protagonists represent French literary figures. A casual examination of a collection of late eighteenth-and early nineteenth-century plays, many of which concern literary figures, led to the initial idea for this study. Conscientious cross-checking was sub sequently done in a number of reference works and contemporary newspapers to obtain complete coverage and to draw up a list of all the plays in which French literary figures appeared as characters. From the total number of such plays, 153 have been used as the primary source of information. They were found scattered either in different collections or as separate copies in various libraries. This source has been supplemented by use of theatrical journals and almanacs giving reviews of some of the plays which were not published.
Designed for researchers and students, Nonlinear Times Series: Theory, Methods and Applications with R Examples familiarizes readers with the principles behind nonlinear time series models—without overwhelming them with difficult mathematical developments. By focusing on basic principles and theory, the authors give readers the background required to craft their own stochastic models, numerical methods, and software. They will also be able to assess the advantages and disadvantages of different approaches, and thus be able to choose the right methods for their purposes. The first part can be seen as a crash course on "classical" time series, with a special emphasis on linear state space models and detailed coverage of random coefficient autoregressions, both ARCH and GARCH models. The second part introduces Markov chains, discussing stability, the existence of a stationary distribution, ergodicity, limit theorems, and statistical inference. The book concludes with a self-contained account on nonlinear state space and sequential Monte Carlo methods. An elementary introduction to nonlinear state space modeling and sequential Monte Carlo, this section touches on current topics, from the theory of statistical inference to advanced computational methods. The book can be used as a support to an advanced course on these methods, or an introduction to this field before studying more specialized texts. Several chapters highlight recent developments such as explicit rate of convergence of Markov chains and sequential Monte Carlo techniques. And while the chapters are organized in a logical progression, the three parts can be studied independently. Statistics is not a spectator sport, so the book contains more than 200 exercises to challenge readers. These problems strengthen intellectual muscles strained by the introduction of new theory and go on to extend the theory in significant ways. The book helps readers hone their skills in nonlinear time series analysis and their applications.
A reference text presenting stochastic processes and a range of approximation and simulation techniques for extracting behavioural information in the context of stochastic population dynamics.
Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific dis ciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathe matics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathematical Sciences (AMS) series, which will focus on advanced textbooks and research level monographs. Preface A successful concurrent numerical simulation requires physics and math ematics to develop and analyze the model, numerical analysis to develop solution methods, and computer science to develop a concurrent implemen tation. No single course can or should cover all these disciplines. Instead, this course on concurrent scientific computing focuses on a topic that is not covered or is insufficiently covered by other disciplines: the algorith mic structure of numerical methods.
A reference to answer all your statistical confidentiality questions. This handbook provides technical guidance on statistical disclosure control and on how to approach the problem of balancing the need to provide users with statistical outputs and the need to protect the confidentiality of respondents. Statistical disclosure control is combined with other tools such as administrative, legal and IT in order to define a proper data dissemination strategy based on a risk management approach. The key concepts of statistical disclosure control are presented, along with the methodology and software that can be used to apply various methods of statistical disclosure control. Numerous examples and guidelines are also featured to illustrate the topics covered. Statistical Disclosure Control: Presents a combination of both theoretical and practical solutions Introduces all the key concepts and definitions involved with statistical disclosure control. Provides a high level overview of how to approach problems associated with confidentiality. Provides a broad-ranging review of the methods available to control disclosure. Explains the subtleties of group disclosure control. Features examples throughout the book along with case studies demonstrating how particular methods are used. Discusses microdata, magnitude and frequency tabular data, and remote access issues. Written by experts within leading National Statistical Institutes. Official statisticians, academics and market researchers who need to be informed and make decisions on disclosure limitation will benefit from this book.
Digital sky surveys, high-precision astrometry from satellite data, deep-space data from orbiting telescopes, and the like have all increased the quantity and quality of astronomical data by orders of magnitude per year for several years. Making sense of this wealth of data requires sophisticated statistical techniques. Fortunately, statistical methodologies have similarly made great strides in recent years. Powerful synergies thus emerge when astronomers and statisticians join in examining astrostatistical problems and approaches. The book begins with an historical overview and tutorial articles on basic cosmology for statisticians and the principles of Bayesian analysis for astronomers. As in earlier volumes in this series, research contributions discussing topics in one field are joined with commentary from scholars in the other. Thus, for example, an overview of Bayesian methods for Poissonian data is joined by discussions of planning astronomical observations with optimal efficiency and nested models to deal with instrumental effects. The principal theme for the volume is the statistical methods needed to model fundamental characteristics of the early universe on its largest scales.
Baseball is not the only sport to use "moneyball." American football fans, teams, and gamblers are increasingly using data to gain an edge against the competition. Professional and college teams use data to help select players and identify team needs. Fans use data to guide fantasy team picks and strategies. Sports bettors and fantasy football players are using data to help inform decision making. This concise book provides a clear introduction to using statistical models to analyze football data. Whether your goal is to produce a winning team, dominate your fantasy football league, qualify for an entry-level football analyst position, or simply learn R and Python using fun example cases, this book is your starting place. You'll learn how to: Apply basic statistical concepts to football datasets Describe football data with quantitative methods Create efficient workflows that offer reproducible results Use data science skills such as web scraping, manipulating data, and plotting data Implement statistical models for football data Link data summaries and model outputs to create reports or presentations using tools such as R Markdown and R Shiny And more
Discrete phenomena are an important aspect of various complex systems, acting both as underlying driving mechanisms and as manifestations of diverse behaviours. However, the characterisation of these discrete phenomena requires models that go beyond those featured in existing books. Largely concerned with mathematical models used to describe time-v
A graduate-level text that examines the semiclassical approach to quantum mechanics Physical systems have been traditionally described in terms of either classical or quantum mechanics. But in recent years, semiclassical methods have developed rapidly, providing deep physical insight and computational tools for quantum dynamics and spectroscopy. In this book, Eric Heller introduces and develops this subject, demonstrating its power with many examples. In the first half of the book, Heller covers relevant aspects of classical mechanics, building from them the semiclassical way through the semiclassical limit of the Feynman path integral. The second half of the book applies this approach to various kinds of spectroscopy, such as molecular spectroscopy and electron imaging and quantum dynamical systems with an emphasis on tunneling. Adopting a distinctly time-dependent viewpoint, Heller argues for semiclassical theories from experimental and theoretical vantage points valuable to research in physics and chemistry. Featuring more than two hundred figures, the book provides a geometric, phase-space, and coordinate-space pathway to greater understanding. Filled with practical examples and applications, The Semiclassical Way to Dynamics and Spectroscopy is a comprehensive presentation of the tools necessary to successfully delve into this unique area of quantum mechanics. A comprehensive approach for using classical mechanics to do quantum mechanics More than two hundred figures to assist intuition Emphasis on semiclassical Green function and wave packet perspective, as well as tunneling and spectroscopy Chapters include quantum mechanics of classically chaotic systems, quantum scarring, and other modern dynamical topics
This is a textbook for advanced undergraduate students and beginning graduate students in applied mathematics. It presents the basic mathematical foundations of stochastic analysis (probability theory and stochastic processes) as well as some important practical tools and applications (e.g., the connection with differential equations, numerical methods, path integrals, random fields, statistical physics, chemical kinetics, and rare events). The book strikes a nice balance between mathematical formalism and intuitive arguments, a style that is most suited for applied mathematicians. Readers can learn both the rigorous treatment of stochastic analysis as well as practical applications in modeling and simulation. Numerous exercises nicely supplement the main exposition.
This book offers a new look at well-established quantification theory for categorical data, referred to by such names as correspondence analysis, dual scaling, optimal scaling, and homogeneity analysis. These multiple identities are a consequence of its large number of properties that allow one to analyze and visualize the strength of variable association in an optimal solution. The book contains modern quantification theory for analyzing the association between two and more categorical variables in a variety of applicative frameworks. Visualization has attracted much attention over the past decades and given rise to controversial opinions. One may consider variations of plotting systems used in the construction of the classic correspondence plot, the biplot, the Carroll-Green-Schaffer scaling, or a new approach in doubled multidimensional space as presented in the book. There are even arguments for no visualization at all. The purpose of this book therefore is to shed new light on time-honored graphical procedures with critical reviews, new ideas, and future directions as alternatives. This stimulating volume is written with fresh new ideas from the traditional framework and the contemporary points of view. It thus offers readers a deep understanding of the ever-evolving nature of quantification theory and its practice. Part I starts with illustrating contingency table analysis with traditional joint graphical displays (symmetric, non-symmetric) and the CGS scaling and then explores logically correct graphs in doubled Euclidean space for both row and column variables. Part II covers a variety of mathematical approaches to the biplot strategy in graphing a data structure, providing a useful source for this modern approach to graphical display. Part II is also concerned with a number of alternative approaches to the joint graphical display such as bimodal cluster analysis and other statistical problems relevant to quantification theory.
Designed both for those who seek an acquaintance with dynamic programming and for those wishing to become experts, this text is accessible to anyone who's taken a course in operations research. It starts with a basic introduction to sequential decision processes and proceeds to the use of dynamic programming in studying models of resource allocation. Subsequent topics include methods for approximating solutions of control problems in continuous time, production control, decision-making in the face of an uncertain future, and inventory control models. The final chapter introduces sequential decision processes that lack fixed planning horizons, and the supplementary chapters treat data structures and the basic properties of convex functions. 1982 edition. Preface to the Dover Edition.
Experienced Guidance on the Technical Issues of Decommissioning ProjectsWritten by one of the original MARSSIM authors, Decommissioning Health Physics: A Handbook for MARSSIM Users, Second Edition is the only book to incorporate all of the requisite technical aspects of planning and executing radiological surveys in support of decommissioning. Exte
The fourth edition of Mechanics of Materials is an in-depth yet accessible introduction to the behavior of solid materials under various stresses and strains. Emphasizing the three key concepts of deformable-body mechanics—equilibrium, material behavior, and geometry of deformation—this popular textbook covers the fundamental concepts of the subject while helping students strengthen their problem-solving skills. Throughout the text, students are taught to apply an effective four-step methodology to solve numerous example problems and understand the underlying principles of each application. Focusing primarily on the behavior of solids under static-loading conditions, the text thoroughly prepares students for subsequent courses in solids and structures involving more complex engineering analyses and Computer-Aided Engineering (CAE). The text provides ample, fully solved practice problems, real-world engineering examples, the equations that correspond to each concept, chapter summaries, procedure lists, illustrations, flow charts, diagrams, and more. This updated edition includes new Python computer code examples, problems, and homework assignments that require only basic programming knowledge.
This book covers the classical theory of Markov chains on general state-spaces as well as many recent developments. The theoretical results are illustrated by simple examples, many of which are taken from Markov Chain Monte Carlo methods. The book is self-contained, while all the results are carefully and concisely proven. Bibliographical notes are added at the end of each chapter to provide an overview of the literature. Part I lays the foundations of the theory of Markov chain on general states-space. Part II covers the basic theory of irreducible Markov chains on general states-space, relying heavily on regeneration techniques. These two parts can serve as a text on general state-space applied Markov chain theory. Although the choice of topics is quite different from what is usually covered, where most of the emphasis is put on countable state space, a graduate student should be able to read almost all these developments without any mathematical background deeper than that needed to study countable state space (very little measure theory is required). Part III covers advanced topics on the theory of irreducible Markov chains. The emphasis is on geometric and subgeometric convergence rates and also on computable bounds. Some results appeared for a first time in a book and others are original. Part IV are selected topics on Markov chains, covering mostly hot recent developments.
This book provides an overview of the application of statistical methods to problems in metrology, with emphasis on modelling measurement processes and quantifying their associated uncertainties. It covers everything from fundamentals to more advanced special topics, each illustrated with case studies from the authors' work in the Nuclear Security Enterprise (NSE). The material provides readers with a solid understanding of how to apply the techniques to metrology studies in a wide variety of contexts. The volume offers particular attention to uncertainty in decision making, design of experiments (DOEx) and curve fitting, along with special topics such as statistical process control (SPC), assessment of binary measurement systems, and new results on sample size selection in metrology studies. The methodologies presented are supported with R script when appropriate, and the code has been made available for readers to use in their own applications. Designed to promote collaboration between statistics and metrology, this book will be of use to practitioners of metrology as well as students and researchers in statistics and engineering disciplines.
SERS was discovered in the 1970s and has since grown enormously in breadth, depth, and understanding. One of the major characteristics of SERS is its interdisciplinary nature: it lies at the boundary between physics, chemistry, colloid science, plasmonics, nanotechnology, and biology. By their very nature, it is impossible to find a textbook that will summarize the principles needed for SERS of these rather dissimilar and disconnected topics. Although a basic understanding of these topics is necessary for research projects in SERS with all its many aspects and applications, they are seldom touched upon as a coherent unit during most undergraduate studies in physics or chemistry. This book intends to fill this existing gap in the literature. It provides an overview of the underlying principles of SERS, from the fundamental understanding of the effect to its potential applications. It is aimed primarily at newcomers to the field, graduate students, researchers or scientists, attracted by the many applications of SERS and plasmonics or its basic science. The emphasis is on concepts and background material for SERS, such as Raman spectroscopy, the physics of plasmons, or colloid science, all of them introduced within the context of SERS, and from where the more specialized literature can be followed. - Represents one of very few books fully dedicated to the topic of surface-enhanced Raman spectroscopy (SERS) - Gives a comprehensive summary of the underlying physical concepts around SERS - Provides a detailed analysis of plasmons and plasmonics
Glass is a material with essentially unlimited application possibilities. This second edition of a comprehensive reference in glass science, points out the correlation between the performance of industrial processes and practice-relevant properties, such as strength and optical properties. Interdisciplinary in his approach, the author discusses both the science and technology, starting with an outline of history and applications, glass structure, and rheology. The sections on properties include mechanical strength and contact resistance, ageing, mechanics of glass processes, the production and control of residual stresses, high-tech products, and current research and development. Applications include glazing, packaging, optical glass, glass fibers for reinforcement, and abrasive tools. The development of touchscreen technology showed how important were the design and resistance of thin flexible glass and these new thin aluminosilicate glasses are also discussed.
Making statistical modeling and inference more accessible to ecologists and related scientists, Introduction to Hierarchical Bayesian Modeling for Ecological Data gives readers a flexible and effective framework to learn about complex ecological processes from various sources of data. It also helps readers get started on building their own statistical models. The text begins with simple models that progressively become more complex and realistic through explanatory covariates and intermediate hidden states variables. When fitting the models to data, the authors gradually present the concepts and techniques of the Bayesian paradigm from a practical point of view using real case studies. They emphasize how hierarchical Bayesian modeling supports multidimensional models involving complex interactions between parameters and latent variables. Data sets, exercises, and R and WinBUGS codes are available on the authors’ website. This book shows how Bayesian statistical modeling provides an intuitive way to organize data, test ideas, investigate competing hypotheses, and assess degrees of confidence of predictions. It also illustrates how conditional reasoning can dismantle a complex reality into more understandable pieces. As conditional reasoning is intimately linked with Bayesian thinking, considering hierarchical models within the Bayesian setting offers a unified and coherent framework for modeling, estimation, and prediction.
This book examines non-Gaussian distributions. It addresses the causes and consequences of non-normality and time dependency in both asset returns and option prices. The book is written for non-mathematicians who want to model financial market prices so the emphasis throughout is on practice. There are abundant empirical illustrations of the models and techniques described, many of which could be equally applied to other financial time series.
This book is a stimulating panoramic tour – quite different from a textbook journey – of the world of statistics in both its theory and practice, for teachers, students and practitioners. At each stop on the tour, the authors investigate unusual and quirky aspects of statistics, highlighting historical, biographical and philosophical dimensions of this field of knowledge. Each chapter opens with perspectives on its theme, often from several points of view. Five original and thought-provoking questions follow. These aim at widening readers’ knowledge and deepening their insight. Scattered among the questions are entertaining puzzles to solve and tantalising paradoxes to explain. Readers can compare their own statistical discoveries with the authors’ detailed answers to all the questions. The writing is lively and inviting, the ideas are rewarding, and the material is extensively cross-referenced. A Panorama of Statistics: Leads readers to discover the fascinations of statistics. Is an enjoyable companion to an undergraduate statistics textbook. Is an enriching source of knowledge for statistics teachers and practitioners. Is unique among statistics books today for its memorable content and engaging style. Lending itself equally to reading through and to dipping into, A Panorama of Statistics will surprise teachers, students and practitioners by the variety of ways in which statistics can capture and hold their interest. Reviews: "As befits the authors' statement that 'this is not a textbook', the structure is unusual. There are twenty-five chapters organised in five sections, each beginning with a brief perspective of a theme in statistics and finishing with five questions related to that theme. The answers provided to the questions, in section six, are as discursive and illuminating as the main body of the text. Even if you are pretty sure you know the answer, it is always worth checking what the authors have to say. Chances are that you will learn something every time. The glimpses and insights given into this enormous and far-reaching discipline succeed in being bewitching, entertaining and inviting; coverage was never the aim." "In summary, this splendid book lives up to the four 'p-values' of its title. It is panoramic in the scope of its survey of statistics, it is full of illuminating perspectives, it sets entertaining and challenging puzzles, and it explores fascinating paradoxes. Read it, enjoy it and learn from it." From Neil Sheldon, Teaching Statistics, volume 9, no. 2, May 2017
This 2004 textbook fills a gap in the literature on general relativity by providing the advanced student with practical tools for the computation of many physically interesting quantities. The context is provided by the mathematical theory of black holes, one of the most elegant, successful, and relevant applications of general relativity. Among the topics discussed are congruencies of timelike and null geodesics, the embedding of spacelike, timelike and null hypersurfaces in spacetime, and the Lagrangian and Hamiltonian formulations of general relativity. Although the book is self-contained, it is not meant to serve as an introduction to general relativity. Instead, it is meant to help the reader acquire advanced skills and become a competent researcher in relativity and gravitational physics. The primary readership consists of graduate students in gravitational physics. It will also be a useful reference for more seasoned researchers working in this field.
This textbook offers a strong introduction to the fundamental concepts of materials science. It conveys the quintessence of this interdisciplinary field, distinguishing it from merely solid-state physics and solid-state chemistry, using metals as model systems to elucidate the relation between microstructure and materials properties. Mittemeijer's Fundamentals of Materials Science provides a consistent treatment of the subject matter with a special focus on the microstructure-property relationship. Richly illustrated and thoroughly referenced, it is the ideal adoption for an entire undergraduate, and even graduate, course of study in materials science and engineering. It delivers a solid background against which more specialized texts can be studied, covering the necessary breadth of key topics such as crystallography, structure defects, phase equilibria and transformations, diffusion and kinetics, and mechanical properties. The success of the first edition has led to this updated and extended second edition, featuring detailed discussion of electron microscopy, supermicroscopy and diffraction methods, an extended treatment of diffusion in solids, and a separate chapter on phase transformation kinetics. “In a lucid and masterly manner, the ways in which the microstructure can affect a host of basic phenomena in metals are described.... By consistently staying with the postulated topic of the microstructure - property relationship, this book occupies a singular position within the broad spectrum of comparable materials science literature .... it will also be of permanent value as a reference book for background refreshing, not least because of its unique annotated intermezzi; an ambitious, remarkable work.” G. Petzow in International Journal of Materials Research. “The biggest strength of the book is the discussion of the structure-property relationships, which the author has accomplished admirably.... In a nutshell, the book should not be looked at as a quick ‘cook book’ type text, but as a serious, critical treatise for some significant time to come.” G.S. Upadhyaya in Science of Sintering. “The role of lattice defects in deformation processes is clearly illustrated using excellent diagrams . Included are many footnotes, ‘Intermezzos’, ‘Epilogues’ and asides within the text from the author’s experience. This ..... soon becomes valued for the interesting insights into the subject and shows the human side of its history. Overall this book provides a refreshing treatment of this important subject and should prove a useful addition to the existing text books available to undergraduate and graduate students and researchers in the field of materials science.” M. Davies in Materials World.
Upon publication, the first edition of the CRC Concise Encyclopedia of Mathematics received overwhelming accolades for its unparalleled scope, readability, and utility. It soon took its place among the top selling books in the history of Chapman & Hall/CRC, and its popularity continues unabated. Yet also unabated has been the d
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