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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 presents both theory of financial data analytics, as well as comprehensive insights into the application of financial data analytics techniques in real financial world situations. It offers solutions on how to logically analyze the enormous amount of structured and unstructured data generated every moment in the finance sector. This data can be used by companies, organizations, and investors to create strategies, as the finance sector rapidly moves towards data-driven optimization. This book provides an efficient resource, addressing all applications of data analytics in the finance sector. International experts from around the globe cover the most important subjects in finance, including data processing, knowledge management, machine learning models, data modeling, visualization, optimization for financial problems, financial econometrics, financial time series analysis, project management, and decision making. The authors provide empirical evidence as examples of specific topics. By combining both applications and theory, the book offers a holistic approach. Therefore, it is a must-read for researchers and scholars of financial economics and finance, as well as practitioners interested in a better understanding of financial data analytics.
This book applies finance to the field of capital theory. While financial economics is a well-established field of study, the specific application of finance to capital theory remains unexplored. It is the first book to comprehensively study this financial application, which also includes modern financial tools such as Economic Value Added (EVA®). A financial application to the problem of the average period of production includes two discussions that unfold naturally from this application. The first one relates to the dual meaning of capital, one as a monetary fund and the other one as physical (capital) goods. The second concerns its implications for business-cycle theories. This second topic (1) provides a solid financial microeconomic foundation for business cycles and, also (2) makes it easy to compare different business-cycle theories across the average period of production dimension. By clarifying the obscure concept of average period of production, the authors make it easier to analyze the similarities with and differences from other business-cycle theories. By connecting finance with capital theory, they provide a new point of view and analysis of the long-standing problems in capital theory as well as other related topics such as the use of neoclassical production functions and theorizing about business cycles. Finally, they emphasize that the relevance of their application rests on both its policy implications and its contributions to contemporary economic theory.
Written by the quantitative research team of Deutsche Bank, the world leader in innovative equity derivative transactions, this book acquaints readers with leading-edge thinking in modeling and hedging these transactions. Equity Derivatives offers a balanced, integrated presentation of theory and practice in equity derivative markets. It provides a theoretical treatment of each new modeling and hedging concept first, and then demonstrates their practical application. The book covers: the newest and fastest-growing class of derivative instruments, fund derivatives; cutting-edge developments in equity derivative modeling; new developments in correlation modeling and understanding volatility skews; and new Web-based implementation/delivery methods. Marcus Overhaus, PhD, Andrew Ferraris, DPhil, Thomas Knudsen, PhD, Frank Mao, PhD, Ross Milward, Laurent Nguyen-Ngoc, PhD, and Gero Schindlmayr, PhD, are members of the Quantitative Research team of Deutsche Bank's Global Equity Division, which is based in London and headed by Dr. Overhaus.
Stefano Gatti describes the theory that underpins this cutting-edge industry, and then provides illustrations and examples from actual practice to illustrate that theory.
This book provides a basic grounding in the use of probability to model random financial phenomena of uncertainty, and is targeted at an advanced undergraduate and graduate level. It should appeal to finance students looking for a firm theoretical guide to the deep end of derivatives and investments. Bankers and finance professionals in the fields of investments, derivatives, and risk management should also find the book useful in bringing probability and finance together. The book contains applications of both discrete time theory and continuous time mathematics, and is extensive in scope. Distribution theory, conditional probability, and conditional expectation are covered comprehensively, and applications to modeling state space securities under market equilibrium are made. Martingale is studied, leading to consideration of equivalent martingale measures, fundamental theorems of asset pricing, change of numeraire and discounting, risk-adjusted and forward-neutral measures, minimal and maximal prices of contingent claims, Markovian models, and the existence of martingale measures preserving the Markov property. Discrete stochastic calculus and multiperiod models leading to no-arbitrage pricing of contingent claims are also to be found in this book, as well as the theory of Markov Chains and appropriate applications in credit modeling. Measure-theoretic probability, moments, characteristic functions, inequalities, and central limit theorems are examined. The theory of risk aversion and utility, and ideas of risk premia are considered. Other application topics include optimal consumption and investment problems and interest rate theory.
A balanced introduction to the theoretical foundations and real-world applications of mathematical finance The ever-growing use of derivative products makes it essential for financial industry practitioners to have a solid understanding of derivative pricing. To cope with the growing complexity, narrowing margins, and shortening life-cycle of the individual derivative product, an efficient, yet modular, implementation of the pricing algorithms is necessary. Mathematical Finance is the first book to harmonize the theory, modeling, and implementation of today's most prevalent pricing models under one convenient cover. Building a bridge from academia to practice, this self-contained text applies theoretical concepts to real-world examples and introduces state-of-the-art, object-oriented programming techniques that equip the reader with the conceptual and illustrative tools needed to understand and develop successful derivative pricing models. Utilizing almost twenty years of academic and industry experience, the author discusses the mathematical concepts that are the foundation of commonly used derivative pricing models, and insightful Motivation and Interpretation sections for each concept are presented to further illustrate the relationship between theory and practice. In-depth coverage of the common characteristics found amongst successful pricing models are provided in addition to key techniques and tips for the construction of these models. The opportunity to interactively explore the book's principal ideas and methodologies is made possible via a related Web site that features interactive Java experiments and exercises. While a high standard of mathematical precision is retained, Mathematical Finance emphasizes practical motivations, interpretations, and results and is an excellent textbook for students in mathematical finance, computational finance, and derivative pricing courses at the upper undergraduate or beginning graduate level. It also serves as a valuable reference for professionals in the banking, insurance, and asset management industries.
This book introduces machine learning methods in finance. It presents a unified treatment of machine learning and various statistical and computational disciplines in quantitative finance, such as financial econometrics and discrete time stochastic control, with an emphasis on how theory and hypothesis tests inform the choice of algorithm for financial data modeling and decision making. With the trend towards increasing computational resources and larger datasets, machine learning has grown into an important skillset for the finance industry. This book is written for advanced graduate students and academics in financial econometrics, mathematical finance and applied statistics, in addition to quants and data scientists in the field of quantitative finance. Machine Learning in Finance: From Theory to Practice is divided into three parts, each part covering theory and applications. The first presents supervised learning for cross-sectional data from both a Bayesian and frequentist perspective. The more advanced material places a firm emphasis on neural networks, including deep learning, as well as Gaussian processes, with examples in investment management and derivative modeling. The second part presents supervised learning for time series data, arguably the most common data type used in finance with examples in trading, stochastic volatility and fixed income modeling. Finally, the third part presents reinforcement learning and its applications in trading, investment and wealth management. Python code examples are provided to support the readers' understanding of the methodologies and applications. The book also includes more than 80 mathematical and programming exercises, with worked solutions available to instructors. As a bridge to research in this emergent field, the final chapter presents the frontiers of machine learning in finance from a researcher's perspective, highlighting how many well-known concepts in statistical physics are likely to emerge as important methodologies for machine learning in finance.
This is truly an interdisciplinary book for knowledge workers in business, finance, management and socio-economic sciences based on fuzzy logic. It serves as a guide to and techniques for forecasting, decision making and evaluations in an environment involving uncertainty, vagueness, impression and subjectivity. Traditional modeling techniques, contrary to fuzzy logic, do not capture the nature of complex systems especially when humans are involved. Fuzzy logic uses human experience and judgement to facilitate plausible reasoning in order to reach a conclusion. Emphasis is on applications presented in the 27 case studies including Time Forecasting for Project Management, New Product Pricing, and Control of a Parasit-Pest System.