Although three decades have passed since the first publication of this book, it is reprinted now as a result of popular demand. The content remains up-to-date and interesting for many researchers as is shown by the many references to it in current publications. The author is one of the leading experts of the field and gives an authoritative treatment of a subject.

This textbook offers an approachable introduction to stochastic processes that explores the four pillars of random walk, branching processes, Brownian motion, and martingales. Building from simple examples, the authors focus on developing context and intuition before formalizing the theory of each topic. This inviting approach illuminates the key ideas and computations in the proofs, forming an ideal basis for further study. Consisting of many short chapters, the book begins with a comprehensive account of the simple random walk in one dimension. From here, different paths may be chosen according to interest. Themes span Poisson processes, branching processes, the Kolmogorov–Chentsov theorem, martingales, renewal theory, and Brownian motion. Special topics follow, showcasing a selection of important contemporary applications, including mathematical finance, optimal stopping, ruin theory, branching random walk, and equations of fluids. Engaging exercises accompany the theory throughout. Random Walk, Brownian Motion, and Martingales is an ideal introduction to the rigorous study of stochastic processes. Students and instructors alike will appreciate the accessible, example-driven approach. A single, graduate-level course in probability is assumed.

'Algorithms to Live By' looks at the simple, precise algorithms that computers use to solve the complex 'human' problems that we face, and discovers what they can tell us about the nature and origin of the mind.

This book is devoted to problems of stochastic control and stopping that are time inconsistent in the sense that they do not admit a Bellman optimality principle. These problems are cast in a game-theoretic framework, with the focus on subgame-perfect Nash equilibrium strategies. The general theory is illustrated with a number of finance applications. In dynamic choice problems, time inconsistency is the rule rather than the exception. Indeed, as Robert H. Strotz pointed out in his seminal 1955 paper, relaxing the widely used ad hoc assumption of exponential discounting gives rise to time inconsistency. Other famous examples of time inconsistency include mean-variance portfolio choice and prospect theory in a dynamic context. For such models, the very concept of optimality becomes problematic, as the decision maker’s preferences change over time in a temporally inconsistent way. In this book, a time-inconsistent problem is viewed as a non-cooperative game between the agent’s current and future selves, with the objective of finding intrapersonal equilibria in the game-theoretic sense. A range of finance applications are provided, including problems with non-exponential discounting, mean-variance objective, time-inconsistent linear quadratic regulator, probability distortion, and market equilibrium with time-inconsistent preferences. Time-Inconsistent Control Theory with Finance Applications offers the first comprehensive treatment of time-inconsistent control and stopping problems, in both continuous and discrete time, and in the context of finance applications. Intended for researchers and graduate students in the fields of finance and economics, it includes a review of the standard time-consistent results, bibliographical notes, as well as detailed examples showcasing time inconsistency problems. For the reader unacquainted with standard arbitrage theory, an appendix provides a toolbox of material needed for the book.

This book discloses a fascinating connection between optimal stopping problems in probability and free-boundary problems. It focuses on key examples and the theory of optimal stopping is exposed at its basic principles in discrete and continuous time covering martingale and Markovian methods. Methods of solution explained range from change of time, space, and measure, to more recent ones such as local time-space calculus and nonlinear integral equations. A chapter on stochastic processes makes the material more accessible. The book will appeal to those wishing to master stochastic calculus via fundamental examples. Areas of application include financial mathematics, financial engineering, and mathematical statistics.

Get to grips with the fundamentals of data mining and predictive analytics with IBM SPSS Modeler About This Book Get up–and-running with IBM SPSS Modeler without going into too much depth. Identify interesting relationships within your data and build effective data mining and predictive analytics solutions A quick, easy–to-follow guide to give you a fundamental understanding of SPSS Modeler, written by the best in the business Who This Book Is For This book is ideal for those who are new to SPSS Modeler and want to start using it as quickly as possible, without going into too much detail. An understanding of basic data mining concepts will be helpful, to get the best out of the book. What You Will Learn Understand the basics of data mining and familiarize yourself with Modeler's visual programming interface Import data into Modeler and learn how to properly declare metadata Obtain summary statistics and audit the quality of your data Prepare data for modeling by selecting and sorting cases, identifying and removing duplicates, combining data files, and modifying and creating fields Assess simple relationships using various statistical and graphing techniques Get an overview of the different types of models available in Modeler Build a decision tree model and assess its results Score new data and export predictions In Detail IBM SPSS Modeler allows users to quickly and efficiently use predictive analytics and gain insights from your data. With almost 25 years of history, Modeler is the most established and comprehensive Data Mining workbench available. Since it is popular in corporate settings, widely available in university settings, and highly compatible with all the latest technologies, it is the perfect way to start your Data Science and Machine Learning journey. This book takes a detailed, step-by-step approach to introducing data mining using the de facto standard process, CRISP-DM, and Modeler's easy to learn “visual programming” style. You will learn how to read data into Modeler, assess data quality, prepare your data for modeling, find interesting patterns and relationships within your data, and export your predictions. Using a single case study throughout, this intentionally short and focused book sticks to the essentials. The authors have drawn upon their decades of teaching thousands of new users, to choose those aspects of Modeler that you should learn first, so that you get off to a good start using proven best practices. This book provides an overview of various popular data modeling techniques and presents a detailed case study of how to use CHAID, a decision tree model. Assessing a model's performance is as important as building it; this book will also show you how to do that. Finally, you will see how you can score new data and export your predictions. By the end of this book, you will have a firm understanding of the basics of data mining and how to effectively use Modeler to build predictive models. Style and approach This book empowers users to build practical & accurate predictive models quickly and intuitively. With the support of the advanced analytics users can discover hidden patterns and trends.This will help users to understand the factors that influence them, enabling you to take advantage of business opportunities and mitigate risks.

Elementary Real Analysis is a core course in nearly all mathematics departments throughout the world. It enables students to develop a deep understanding of the key concepts of calculus from a mature perspective. Elements of Real Analysis is a student-friendly guide to learning all the important ideas of elementary real analysis, based on the author's many years of experience teaching the subject to typical undergraduate mathematics majors. It avoids the compact style of professional mathematics writing, in favor of a style that feels more comfortable to students encountering the subject for the first time. It presents topics in ways that are most easily understood, yet does not sacrifice rigor or coverage. In using this book, students discover that real analysis is completely deducible from the axioms of the real number system. They learn the powerful techniques of limits of sequences as the primary entry to the concepts of analysis, and see the ubiquitous role sequences play in virtually all later topics. They become comfortable with topological ideas, and see how these concepts help unify the subject. Students encounter many interesting examples, including "pathological" ones, that motivate the subject and help fix the concepts. They develop a unified understanding of limits, continuity, differentiability, Riemann integrability, and infinite series of numbers and functions.

First published in 2004, this is a rigorous but user-friendly book on the application of stochastic control theory to economics. A distinctive feature of the book is that mathematical concepts are introduced in a language and terminology familiar to graduate students of economics. The standard topics of many mathematics, economics and finance books are illustrated with real examples documented in the economic literature. Moreover, the book emphasises the dos and don'ts of stochastic calculus, cautioning the reader that certain results and intuitions cherished by many economists do not extend to stochastic models. A special chapter (Chapter 5) is devoted to exploring various methods of finding a closed-form representation of the value function of a stochastic control problem, which is essential for ascertaining the optimal policy functions. The book also includes many practice exercises for the reader. Notes and suggested readings are provided at the end of each chapter for more references and possible extensions.

"Optimal Mean Reversion Trading: Mathematical Analysis and Practical Applications provides a systematic study to the practical problem of optimal trading in the presence of mean-reverting price dynamics. It is self-contained and organized in its presentation, and provides rigorous mathematical analysis as well as computational methods for trading ETFs, options, futures on commodities or volatility indices, and credit risk derivatives. This book offers a unique financial engineering approach that combines novel analytical methodologies and applications to a wide array of real-world examples. It extracts the mathematical problems from various trading approaches and scenarios, but also addresses the practical aspects of trading problems, such as model estimation, risk premium, risk constraints, and transaction costs. The explanations in the book are detailed enough to capture the interest of the curious student or researcher, and complete enough to give the necessary background material for further exploration into the subject and related literature. This book will be a useful tool for anyone interested in financial engineering, particularly algorithmic trading and commodity trading, and would like to understand the mathematically optimal strategies in different market environments."--