Bøger af Petr Hajek

This book presents the state-of-the-art applications of machine learning in the finance domain with a focus on financial product modeling, which aims to advance the model performance and minimize risk and uncertainty. It provides both practical and managerial implications of financial and managerial decision support systems which capture a broad range of financial data traits. It also serves as a guide for the implementation of risk-adjusted financial product pricing systems, while adding a significant supplement to the financial literacy of the investigated study.The book covers advanced machine learning techniques, such as Support Vector Machine, Neural Networks, Random Forest, K-Nearest Neighbors, Extreme Learning Machine, Deep Learning Approaches, and their application to finance datasets. It also leverages real-world financial instances to practice business product modeling and data analysis. Software code, such as MATLAB, Python and/or R including datasets within a broad range of financial domain are included for more rigorous practice.The book primarily aims at providing graduate students and researchers with a roadmap for financial data analysis. It is also intended for a broad audience, including academics, professional financial analysts, and policy-makers who are involved in forecasting, modeling, trading, risk management, economics, credit risk, and portfolio management.

One of the fundamental questions of Banach space theory is whether every Banach space has a basis. A space with a basis gives us the feeling of familiarity and concreteness, and perhaps a chance to attempt the classification of all Banach spaces and other problems.The main goals of this book are to: introduce the reader to some of the basic concepts, results and applications of biorthogonal systems in infinite dimensional geometry of Banach spaces, and in topology and nonlinear analysis in Banach spaces; to do so in a manner accessible to graduate students and researchers who have a foundation in Banach space theory; expose the reader to some current avenues of research in biorthogonal systems in Banach spaces; provide notes and exercises related to the topic, as well as suggesting open problems and possible directions of research.The intended audience will have a basic background in functional analysis. The authors have included numerous exercises, as well as open problems that point to possible directions of research.

This book introduces the basic principles of functional analysis and areas of Banach space theory that are close to nonlinear analysis and topology. The text can be used in graduate courses or for independent study. It includes a large number of exercises of different levels of difficulty, accompanied by hints.

The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear analysis and applications in various fields, such as optimization, control theory, systems theory, mechanics, engineering, and other sciences. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of nonlinear analysis. Contributions which are on the borderline of nonlinear analysis and related fields and which stimulate further research at the crossroads of these areas are particularly welcome. Editor-in-ChiefJurgen Appell, Wurzburg, Germany Honorary and Advisory EditorsCatherine Bandle, Basel, SwitzerlandAlain Bensoussan, Richardson, Texas, USAAvner Friedman, Columbus, Ohio, USAUmberto Mosco, Worcester, Massachusetts, USALouis Nirenberg, New York, USAAlfonso Vignoli, Rome, Italy Editorial BoardManuel del Pino, Bath, UK, and Santiago, ChileMikio Kato, Nagano, JapanWojciech Kryszewski, Torun, PolandVicentiu D. Radulescu, Krakow, PolandSimeon Reich, Haifa, Israel Please submit book proposals to Jurgen Appell. Titles in planning include Lucio Damascelli and Filomena Pacella, Morse Index of Solutions of Nonlinear Elliptic Equations (2019)Tomasz W. Dlotko and Yejuan Wang, Critical Parabolic-Type Problems (2019)Rafael Ortega, Periodic Differential Equations in the Plane: A Topological Perspective (2019)Ireneo Peral Alonso and Fernando Soria, Elliptic and Parabolic Equations Involving the Hardy-Leray Potential (2020)Cyril Tintarev, Profile Decompositions and Cocompactness: Functional-Analytic Theory of Concentration Compactness (2020)Takashi Suzuki, Semilinear Elliptic Equations: Classical and Modern Theories (2021)

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the third publication in the Perspectives in Logic series, is a much-needed monograph on the metamathematics of first-order arithmetic. The authors pay particular attention to subsystems (fragments) of Peano arithmetic and give the reader a deeper understanding of the role of the axiom schema of induction and of the phenomenon of incompleteness. The reader is only assumed to know the basics of mathematical logic, which are reviewed in the preliminaries. Part I develops parts of mathematics and logic in various fragments. Part II is devoted to incompleteness. Finally, Part III studies systems that have the induction schema restricted to bounded formulas (bounded arithmetic).

This book introduces the reader to linear functional analysis and to related parts of infinite-dimensional Banach space theory. Coverage includes Radon-Nikodym property, finite-dimensional spaces and local theory on tensor products, and more.

This book introduces the reader to some of the basic concepts, results and applications of biorthogonal systems in infinite dimensional geometry of Banach spaces, and in topology and nonlinear analysis in Banach spaces. It achieves this in a manner accessible to graduate students and researchers who have a foundation in Banach space theory.

This book presents a systematic treatment of deductive aspects and structures of fuzzy logic understood as many valued logic sui generis.

This book presents a systematic treatment of deductive aspects and structures of fuzzy logic understood as many valued logic sui generis.