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Portfolio Optimization (Chapman and Hall/CRC Financial Mathematics Series)
by Michael J. BestEschewing a more theoretical approach, Portfolio Optimization shows how the mathematical tools of linear algebra and optimization can quickly and clearly formulate important ideas on the subject. This practical book extends the concepts of the Markowitz "budget constraint only" model to a linearly constrained model.Only requiring elementary linear algebra, the text begins with the necessary and sufficient conditions for optimal quadratic minimization that is subject to linear equality constraints. It then develops the key properties of the efficient frontier, extends the results to problems with a risk-free asset, and presents Sharpe ratios and implied risk-free rates. After focusing on quadratic programming, the author discusses a constrained portfolio optimization problem and uses an algorithm to determine the entire (constrained) efficient frontier, its corner portfolios, the piecewise linear expected returns, and the piecewise quadratic variances. The final chapter illustrates infinitely many implied risk returns for certain market portfolios.Drawing on the author’s experiences in the academic world and as a consultant to many financial institutions, this text provides a hands-on foundation in portfolio optimization. Although the author clearly describes how to implement each technique by hand, he includes several MATLAB® programs designed to implement the methods and offers these programs on the accompanying downloadable resources.
Portfolio Optimization and Performance Analysis (Chapman and Hall/CRC Financial Mathematics Series)
by Jean-Luc PrigentIn answer to the intense development of new financial products and the increasing complexity of portfolio management theory, Portfolio Optimization and Performance Analysis offers a solid grounding in modern portfolio theory. The book presents both standard and novel results on the axiomatics of the individual choice in an uncertain framework, cont
Portfolio Rebalancing (Chapman and Hall/CRC Financial Mathematics)
by Edward E. QianThe goal of Portfolio Rebalancing is to provide mathematical and empirical analysis of the effects of portfolio rebalancing on portfolio returns and risks. The mathematical analysis answers the question of when and why fixed-weight portfolios might outperform buy-and-hold portfolios based on volatilities and returns. The empirical analysis, aided by mathematical insights, will examine the effects of portfolio rebalancing in capital markets for asset allocation portfolios and portfolios of stocks, bonds, and commodities.
Portfolio Selection
by Harry M. MarkowitzThis is a classic book, representing the first major breakthrough in the field of modern financial theory. In effect, it created the mathematics of portfolio selection in a model which has turned out to be the indispensable building block from which the theory of the demand for risky securities is constructed. It also became an essential reference for individuals and financial institutions actually selecting optimal portfolios. Long out of print and unavailable to numerous recent entrants to both financial theory and financial practice, this new edition leaves the existing text as it stands but adds substantial new material including a new bibliography and a fascinating biographical piece on the birth of the field of finance.
Poset Codes: Partial Orders, Metrics and Coding Theory (SpringerBriefs in Mathematics)
by Marcelo Firer Marcelo Muniz S. Alves Jerry Anderson Pinheiro Luciano PanekThis book offers an organized and systematic approach to poset metrics and codes. Poset metrics, or metrics on a vector field determined by a partial order over a finite set, were first introduced in the mid-1990s by the mathematicians Richard A. Brualdi, Janine S. Graves and K. Mark Lawrence, and to date the relevant knowledge on this subject was spread over more than two hundred research papers. Poset metrics generalizes both the standard Hamming metric – the most important metric used in the context of coding theory – and the Niederreiter-Rosenbloom-Tsfasman metric, which is an ultrametric. Conceived to be as self-contained as possible, the book starts from basic concepts of coding theory and advances towards coding theory for poset metrics and generalizations. Each chapter includes a survey of the topic presented and a list of exercises, drawn in part from recently proven results. This work will appeal to researchers and graduate students alike, particularly those in the fields of Mathematics, Electrical Engineering and Computer Sciences, with an interest in discrete geometry and coding theory.
Posing and Solving Mathematical Problems
by Jeremy Kilpatrick Patricio Felmer Erkki PehkonenThis book collects recent research on posing and solving mathematical problems. Rather than treating these two crucial aspects of school mathematics as separate areas of study, the authors approach them as a unit where both areas are measured on equal grounds in relation to each other. The contributors are from a vast variety of countries and with a wide range of experience; it includes the work from many of the leading researchers in the area and an important number of young researchers. The book is divided in three parts, one directed to new research perspectives and the other two directed to teachers and students, respectively.
Positioning and Navigation Using Machine Learning Methods (Navigation: Science and Technology #14)
by Kegen YuThis is the first book completely dedicated to positioning and navigation using machine learning methods. It deals with ground, aerial, and space positioning and navigation for pedestrians, vehicles, UAVs, and LEO satellites. Most of the major machine learning methods are utilized, including supervised learning, unsupervised learning, deep learning, and reinforcement learning. The book presents both fundamentals and in-depth studies as well as practical examples in positioning and navigation. Extensive data processing and experimental results are provided in the major chapters through conducting experimental campaigns or using in-situ measurements.
Positive Aging and Precarity: Theory, Policy, and Social Reality within a Comparative German Context (International Perspectives on Aging #21)
by Irina Catrinel CrăciunThis book explores positive aging through the lens of precarity, aiming to ground positive aging theories in current social contexts. In recent years, research on aging has been branded by growing disagreements between supporters of the successful aging model and critical gerontologists who highlight the widening inequalities, disadvantages and precarity that characterize old age. This book comes to fill a gap in knowledge by offering an alternative view on positive aging, informed by precarity and its impact on projections concerning aging.The first part of the book places aging in broader theoretical and empirical context, exploring the complex links between views on aging, successful aging theories, policy and social reality. The second part uses results from a qualitative research conducted in Germany to illustrate the dissonance between successful aging ideals and both negative and positive views on aging as well as aging preparation strategies inspired by precarity. Findings from this section provide a solid starting point for comparisons with countries that are both similar and different from Germany in terms of welfare regimes and aging policies. The final part of the book discusses the psychological implications of these findings within and beyond the German case study and outlines potential solutions for practice. This book provides health psychologists, gerontologists, sociologists, social workers, health professionals as well as students and aging individuals themselves with better understanding of the meaning of aging in precarious times and builds confidence about aging well despite precarity.
Positive Definite Matrices (Princeton Series in Applied Mathematics #24)
by Rajendra BhatiaThis book represents the first synthesis of the considerable body of new research into positive definite matrices. These matrices play the same role in noncommutative analysis as positive real numbers do in classical analysis. They have theoretical and computational uses across a broad spectrum of disciplines, including calculus, electrical engineering, statistics, physics, numerical analysis, quantum information theory, and geometry. Through detailed explanations and an authoritative and inspiring writing style, Rajendra Bhatia carefully develops general techniques that have wide applications in the study of such matrices. Bhatia introduces several key topics in functional analysis, operator theory, harmonic analysis, and differential geometry--all built around the central theme of positive definite matrices. He discusses positive and completely positive linear maps, and presents major theorems with simple and direct proofs. He examines matrix means and their applications, and shows how to use positive definite functions to derive operator inequalities that he and others proved in recent years. He guides the reader through the differential geometry of the manifold of positive definite matrices, and explains recent work on the geometric mean of several matrices. Positive Definite Matrices is an informative and useful reference book for mathematicians and other researchers and practitioners. The numerous exercises and notes at the end of each chapter also make it the ideal textbook for graduate-level courses.
Positive Linear Maps of Operator Algebras
by Erling StørmerThis volume, setting out the theory of positive maps as it stands today, reflects the rapid growth in this area of mathematics since it was recognized in the 1990s that these applications of C*-algebras are crucial to the study of entanglement in quantum theory. The author, a leading authority on the subject, sets out numerous results previously unpublished in book form. In addition to outlining the properties and structures of positive linear maps of operator algebras into the bounded operators on a Hilbert space, he guides readers through proofs of the Stinespring theorem and its applications to inequalities for positive maps. The text examines the maps' positivity properties, as well as their associated linear functionals together with their density operators. It features special sections on extremal positive maps and Choi matrices. In sum, this is a vital publication that covers a full spectrum of matters relating to positive linear maps, of which a large proportion is relevant and applicable to today's quantum information theory. The latter sections of the book present the material in finite dimensions, while the text as a whole appeals to a wider and more general readership by keeping the mathematics as elementary as possible throughout.
Positive Operators and Fixed-Point Theorems with Applications (Industrial and Applied Mathematics)
by S. A. Mohiuddine Anupam Das Dragan S. DjordjevićThis book presents original research on the theory of positive operators, alongside fixed-point theorems and their diverse applications. It introduces various positive operators and explores their approximation properties, including Korovkin-type theorems, Voronovskaja-type results, convergence rate, and other related findings. Additionally, the book addresses the existence of solutions for various differential and integral equations in different Banach spaces by using Darbo-type fixed-point theorems. This book also presents an interplay between positive operators and fixed-point theory. Each chapter is self-contained, addressing a current problem and outlining solutions and potential applications. The chapters provide sufficient background to ensure that new definitions and results can be understood independently.
Positive Trigonometric Polynomials and Signal Processing Applications
by Bogdan DumitrescuPositive Trigonometric Polynomials and Signal Processing Applications has two parts: theory and applications. The theory of sum-of-squares trigonometric polynomials is presented unitarily based on the concept of Gram matrix (extended to Gram pair or Gram set). The presentation starts by giving the main results for univariate polynomials, which are later extended and generalized for multivariate polynomials. The applications part is organized as a collection of related problems that use systematically the theoretical results. All the problems are brought to a semidefinite programming form, ready to be solved with algorithms freely available, like those from the library SeDuMi.
Positives Altern und Prekarität: Theorie, Politik und soziale Realität im vergleichenden deutschen Kontext
by Irina Catrinel CrăciunDieses Buch untersucht positives Altern aus der Perspektive der Prekarität und zielt darauf ab, Theorien des positiven Alterns in aktuellen sozialen Kontexten zu verankern. In den letzten Jahren war die Forschung zum Thema Altern von wachsenden Meinungsverschiedenheiten zwischen Befürwortern des Modells des erfolgreichen Alterns und kritischen Gerontologen geprägt, die auf die zunehmenden Ungleichheiten, Benachteiligungen und die Prekarität hinweisen, die das Alter charakterisieren. Dieses Buch schließt eine Wissenslücke, indem es eine alternative Sichtweise auf positives Altern bietet, die durch Prekarität und deren Auswirkungen auf Projektionen zum Thema Altern informiert ist. Der erste Teil des Buches stellt das Altern in einen breiteren theoretischen und empirischen Kontext und untersucht die komplexen Zusammenhänge zwischen Ansichten über das Altern, Theorien des erfolgreichen Alterns, Politik und sozialer Realität. Der zweite Teil nutzt Ergebnisse einer qualitativen Forschung, die in Deutschland durchgeführt wurde, um die Diskrepanz zwischen den Idealen des erfolgreichen Alterns und sowohl negativen als auch positiven Ansichten über das Altern sowie Vorbereitungsstrategien auf das Altern, die durch Prekarität inspiriert sind, zu veranschaulichen. Die Ergebnisse dieses Abschnitts bieten einen soliden Ausgangspunkt für Vergleiche mit Ländern, die hinsichtlich der Wohlfahrtsregime und der Alternspolitiken sowohl Ähnlichkeiten als auch Unterschiede zu Deutschland aufweisen. Der abschließende Teil des Buches erörtert die psychologischen Implikationen dieser Ergebnisse innerhalb und außerhalb der deutschen Fallstudie und skizziert mögliche Lösungen für die Praxis. Dieses Buch bietet Gesundheitspsychologen, Gerontologen, Soziologen, Sozialarbeitern, Gesundheitsfachkräften sowie Studierenden und den älteren Menschen selbst ein besseres Verständnis für die Bedeutung des Alterns in prekären Zeiten und stärkt das Vertrauen, trotz Prekarität gut zu altern.
Positivity and Noncommutative Analysis: Festschrift in Honour of Ben de Pagter on the Occasion of his 65th Birthday (Trends in Mathematics)
by Jan Van Neerven Gerard Buskes Marcel De Jeu Peter Dodds Anton Schep Fedor Sukochev Anthony WicksteadCapturing the state of the art of the interplay between positivity, noncommutative analysis, and related areas including partial differential equations, harmonic analysis, and operator theory, this volume was initiated on the occasion of the Delft conference in honour of Ben de Pagter's 65th birthday. It will be of interest to researchers in positivity, noncommutative analysis, and related fields. Contributions by Shavkat Ayupov, Amine Ben Amor, Karim Boulabiar, Qingying Bu, Gerard Buskes, Martijn Caspers, Jurie Conradie, Garth Dales, Marcel de Jeu, Peter Dodds, Theresa Dodds, Julio Flores, Jochen Glück, Jacobus Grobler, Wolter Groenevelt, Markus Haase, Klaas Pieter Hart, Francisco Hernández, Jamel Jaber, Rien Kaashoek, Turabay Kalandarov, Anke Kalauch, Arkady Kitover, Erik Koelink, Karimbergen Kudaybergenov, Louis Labuschagne, Yongjin Li, Nick Lindemulder, Emiel Lorist, Qi Lü, Miek Messerschmidt, Susumu Okada, Mehmet Orhon, Denis Potapov, Werner Ricker, Stephan Roberts, Pablo Román, Anton Schep, Claud Steyn, Fedor Sukochev, James Sweeney, Guido Sweers, Pedro Tradacete, Jan Harm van der Walt, Onno van Gaans, Jan van Neerven, Arnoud van Rooij, Freek van Schagen, Dominic Vella, Mark Veraar, Anthony Wickstead, Marten Wortel, Ivan Yaroslavtsev, and Dmitriy Zanin.
Positivity and its Applications: Positivity X, 8-12 July 2019, Pretoria, South Africa (Trends in Mathematics)
by Eder Kikianty Mokhwetha Mabula Miek Messerschmidt Jan Harm van der Walt Marten WortelThis proceedings volume features selected contributions from the conference Positivity X. The field of positivity deals with ordered mathematical structures and their applications. At the biannual series of Positivity conferences, the latest developments in this diverse field are presented. The 2019 edition was no different, with lectures covering a broad spectrum of topics, including vector and Banach lattices and operators on such spaces, abstract stochastic processes in an ordered setting, the theory and applications of positive semi-groups to partial differential equations, Hilbert geometries, positivity in Banach algebras and, in particular, operator algebras, as well as applications to mathematical economics and financial mathematics. The contributions in this book reflect the variety of topics discussed at the conference. They will be of interest to researchers in functional analysis, operator theory, measure and integration theory, operator algebras, and economics. Positivity X was dedicated to the memory of our late colleague and friend, Coenraad Labuschagne. His untimely death in 2018 came as an enormous shock to the Positivity community. He was a prominent figure in the Positivity community and was at the forefront of the recent development of abstract stochastic processes in a vector lattice context.
Positivity in Arakelov Geometry over Adelic Curves: Hilbert-Samuel Formula and Equidistribution Theorem (Progress in Mathematics #355)
by Huayi Chen Atsushi MoriwakiThis monograph presents new research on Arakelov geometry over adelic curves, a novel theory of arithmetic geometry developed by the authors. It explores positivity conditions and establishes the Hilbert-Samuel formula and the equidistribution theorem in the context of adelic curves. Connections with several classical topics in Arakelov geometry and Diophantine geometry are highlighted, such as the arithmetic Hilbert-Samuel formula, positivity of line bundles, equidistribution of small subvarieties, and theorems resembling the Bogomolov conjecture. Detailed proofs and explanations are provided to ensure the text is accessible to both graduate students and experienced researchers.
Possibility Theory for the Design of Information Fusion Systems (Information Fusion and Data Science)
by Éloi Bossé Basel SolaimanThis practical guidebook describes the basic concepts, the mathematical developments, and the engineering methodologies for exploiting possibility theory for the computer-based design of an information fusion system where the goal is decision support for industries in smart ICT (information and communications technologies). This exploitation of possibility theory improves upon probability theory, complements Dempster-Shafer theory, and fills an important gap in this era of Big Data and Internet of Things.The book discusses fundamental possibilistic concepts: distribution, necessity measure, possibility measure, joint distribution, conditioning, distances, similarity measures, possibilistic decisions, fuzzy sets, fuzzy measures and integrals, and finally, the interrelated theories of uncertainty..uncertainty. These topics form an essential tour of the mathematical tools needed for the latter chapters of the book. These chapters present applications related to decision-making and pattern recognition schemes, and finally, a concluding chapter on the use of possibility theory in the overall challenging design of an information fusion system. This book will appeal to researchers and professionals in the field of information fusion and analytics, information and knowledge processing, smart ICT, and decision support systems.
Post-Katrina Recovery of the Housing Market Along the Mississippi Gulf Coast
by Kevin F. Mccarthy Mark HansonIn summer 2006, the Commission on Recovery, Rebuilding, and Renewal asked the RAND Gulf States Policy Institute to describe the state of the pre-Hurricane Katrina housing markets in Mississippi's three coastal counties, to estimate the damage the storm did to their housing markets, to describe the status of the recovery effort, and to identify problems that might inhibit it. This report publishes the findings.
Post-Optimal Analysis in Linear Semi-Infinite Optimization
by Miguel A. Goberna Marco A. LópezPost-Optimal Analysis in Linear Semi-Infinite Optimization examines the following topics in regards to linear semi-infinite optimization: modeling uncertainty, qualitative stability analysis, quantitative stability analysis and sensitivity analysis. Linear semi-infinite optimization (LSIO) deals with linear optimization problems where the dimension of the decision space or the number of constraints is infinite. The authors compare the post-optimal analysis with alternative approaches to uncertain LSIO problems and provide readers with criteria to choose the best way to model a given uncertain LSIO problem depending on the nature and quality of the data along with the available software. This work also contains open problems which readers will find intriguing a challenging. Post-Optimal Analysis in Linear Semi-Infinite Optimization is aimed toward researchers, graduate and post-graduate students of mathematics interested in optimization, parametric optimization and related topics.
Post-Pandemic Economic and Social Development: Recovery, Challenges, and Policy in Malaysia (Routledge Studies in the Growth Economies of Asia)
by Muzalwana Abdul Talib Ahmad Farid Osman Bahri, Elya Nabila AbdulThis book explores Malaysia’s experience during the COVID-19 pandemic, analyzing the profound economic and societal challenges faced from 2020 to 2022.The coverage of Malaysia’s post-pandemic recovery provides valuable insights into ongoing global issues. Contributors to this book address a wide range of topics, including unemployment, monetary and trade policies, tourism, human capital development, and women’s labor participation. They also examine the rise of the gig economy, poverty alleviation efforts, and social safety nets. By presenting model applications and empirical research, the book offers data-driven policy advice to handle challenges that arise from pandemics, such as rising inflation, supply chain disruptions, disparities and sustainability issues.This book will interest academics and researchers in the field of econometrics, Asian economics and Malaysian studies. It will also act as a useful guide for NGOs, practitioners, public administrators, and economic policymakers involved in post-COVID-19 economic revival and policy development.
Post-Shrinkage Strategies in Statistical and Machine Learning for High Dimensional Data
by Syed Ejaz Ahmed Feryaal Ahmed Bahadir YüzbaşıThis book presents some post-estimation and predictions strategies for the host of useful statistical models with applications in data science. It combines statistical learning and machine learning techniques in a unique and optimal way. It is well-known that machine learning methods are subject to many issues relating to bias, and consequently the mean squared error and prediction error may explode. For this reason, we suggest shrinkage strategies to control the bias by combining a submodel selected by a penalized method with a model with many features. Further, the suggested shrinkage methodology can be successfully implemented for high dimensional data analysis. Many researchers in statistics and medical sciences work with big data. They need to analyse this data through statistical modelling. Estimating the model parameters accurately is an important part of the data analysis. This book may be a repository for developing improve estimation strategies for statisticians. This book will help researchers and practitioners for their teaching and advanced research, and is an excellent textbook for advanced undergraduate and graduate courses involving shrinkage, statistical, and machine learning. The book succinctly reveals the bias inherited in machine learning method and successfully provides tools, tricks and tips to deal with the bias issue. Expertly sheds light on the fundamental reasoning for model selection and post estimation using shrinkage and related strategies. This presentation is fundamental, because shrinkage and other methods appropriate for model selection and estimation problems and there is a growing interest in this area to fill the gap between competitive strategies. Application of these strategies to real life data set from many walks of life. Analytical results are fully corroborated by numerical work and numerous worked examples are included in each chapter with numerous graphs for data visualization. The presentation and style of the book clearly makes it accessible to a broad audience. It offers rich, concise expositions of each strategy and clearly describes how to use each estimation strategy for the problem at hand. This book emphasizes that statistics/statisticians can play a dominant role in solving Big Data problems, and will put them on the precipice of scientific discovery. The book contributes novel methodologies for HDDA and will open a door for continued research in this hot area. The practical impact of the proposed work stems from wide applications. The developed computational packages will aid in analyzing a broad range of applications in many walks of life.
Post-cosmopolitan Cities
by Caroline Humphrey Vera SkvirskajaExamining the way people imagine and interact in their cities, this book explores the post-cosmopolitan city. The contributors consider the effects of migration, national, and religious revivals (with their new aesthetic sensibilities), the dispositions of marginalized economic actors, and globalized tourism on urban sociality. The case studies here share the situation of having been incorporated in previous political regimes (imperial, colonial, socialist) that one way or another created their own kind of cosmopolitanism, and now these cities are experiencing the aftermath of these regimes while being exposed to new national politics and migratory flows of people.
Postmodern Fermi Liquids (Springer Theses)
by Umang MehtaThis thesis develops a new approach to Fermi liquids based on the mathematical formalism of coadjoint orbits, allowing Landau’s Fermi liquid theory to be recast in a simple and elegant way as a field theory. The theory of Fermi liquids is a cornerstone of condensed matter physics with many applications, but efforts to cast Landau’s Fermi liquid theory in the modern language of effective field theory suffer from technical and conceptual difficulties: the Fermi surface seems to defy a simple effective field theory description. This thesis reviews the recently-developed formalism for Fermi liquids that exploits an underlying structure described by the group of canonical transformations of a single particle phase space. This infinite-dimensional group governs the space of states of zero temperature Fermi liquids and allows one to write down a nonlinear, bosonized action that reproduces Landau’s kinetic theory in the classical limit. The thesis then describes how that Fermi liquid theory can essentially be thought of as a non-trivial representation of the Lie group of canonical transformations, bringing it within the fold of effective theories in many-body physics whose structure is determined by symmetries. After analyzing the benefits and limitations of this geometric formalism, pathways to extensions of the formalism to include superconducting and magnetic phases, as well as applications to the problem of non-Fermi liquids, are discussed. The thesis begins with a pedagogical review of Fermi liquid theory and concludes with a discussion on possible future directions for Fermi surface physics, and more broadly, the usefulness of diffeomorphism groups in condensed matter physics.
Potential Game Theory
by Quang Duy Lã Yong Huat Chew Boon-Hee SoongThis book offers a thorough examination of potential game theory and its applications in radio resource management for wireless communications systems and networking. The book addresses two major research goals: how to identify a given game as a potential game, and how to design the utility functions and the potential functions with certain special properties in order to formulate a potential game. After proposing a unifying mathematical framework for the identification of potential games, the text surveys existing applications of this technique within wireless communications and networking problems found in OFDMA 3G/4G/WiFi networks, as well as next-generation systems such as cognitive radios and dynamic spectrum access networks. Professionals interested in understanding the theoretical aspect of this specialized field will find Potential Game Theory a valuable resource, as will advanced-level engineering students. It paves the way for extensive and rigorous research exploration on a topic whose capacity for practical applications is vast but not yet fully exploited.
Potential Method in Mathematical Theories of Multi-Porosity Media (Interdisciplinary Applied Mathematics #51)
by Merab SvanadzeThis monograph explores the application of the potential method to three-dimensional problems of the mathematical theories of elasticity and thermoelasticity for multi-porosity materials. These models offer several new possibilities for the study of important problems in engineering and mechanics involving multi-porosity materials, including geological materials (e.g., oil, gas, and geothermal reservoirs); manufactured porous materials (e.g., ceramics and pressed powders); and biomaterials (e.g., bone and the human brain). Proceeding from basic to more advanced material, the first part of the book begins with fundamental solutions in elasticity, followed by Galerkin-type solutions and Green’s formulae in elasticity and problems of steady vibrations, quasi-static, and pseudo-oscillations for multi-porosity materials. The next part follows a similar format for thermoelasticity, concluding with a chapter on problems of heat conduction for rigid bodies. The final chapter then presents a number of open research problems to which the results presented here can be applied. All results discussed by the author have not been published previously and offer new insights into these models.Potential Method in Mathematical Theories of Multi-Porosity Media will be a valuable resource for applied mathematicians, mechanical, civil, and aerospace engineers, and researchers studying continuum mechanics. Readers should be knowledgeable in classical theories of elasticity and thermoelasticity.