A unified, comprehensive, and up-to-date introduction to the analytical and numerical tools for solving dynamic economic problems. This book offers a unified, comprehensive, and up-to-date treatment of analytical and numerical tools for solving dynamic economic problems. The focus is on introducing recursive methods—an important part of every economist's set of tools—and readers will learn to apply recursive methods to a variety of dynamic economic problems. The book is notable for its combination of theoretical foundations and numerical methods. Each topic is first described in theoretical terms, with explicit definitions and rigorous proofs; numerical methods and computer codes to implement these methods follow. Drawing on the latest research, the book covers such cutting-edge topics as asset price bubbles, recursive utility, robust control, policy analysis in dynamic New Keynesian models with the zero lower bound on interest rates, and Bayesian estimation of dynamic stochastic general equilibrium (DSGE) models. The book first introduces the theory of dynamical systems and numerical methods for solving dynamical systems, and then discusses the theory and applications of dynamic optimization. The book goes on to treat equilibrium analysis, covering a variety of core macroeconomic models, and such additional topics as recursive utility (increasingly used in finance and macroeconomics), dynamic games, and recursive contracts. The book introduces Dynare, a widely used software platform for handling a range of economic models; readers will learn to use Dynare for numerically solving DSGE models and performing Bayesian estimation of DSGE models. Mathematical appendixes present all the necessary mathematical concepts and results. Matlab codes used to solve examples are indexed and downloadable from the book's website. A solutions manual for students is available for sale from the MIT Press; a downloadable instructor's manual is available to qualified instructors.

This manual includes solutions to the odd-numbered exercises in Economic Dynamics in Discrete Time. Some exercises are purely analytical, while others require numerical methods. Computer codes are provided for most problems. Many exercises ask the reader to apply the methods learned in a chapter to solve related problems, but some exercises ask the reader to complete missing steps in the proof of a theorem or in the solution of an example in the book.

This rigorous but brilliantly lucid book presents a self-contained treatment of modern economic dynamics. Stokey, Lucas, and Prescott develop the basic methods of recursive analysis and illustrate the many areas where they can usefully be applied.

This new book will be welcomed by econometricians and students of econometrics everywhere. Introducing discrete time modelling techniques and bridging the gap between economics and econometric literature, this ambitious book is sure to be an invaluable resource for all those to whom the terms unit roots, cointegration and error correction forms, ch

A unified and comprehensive introduction to the analytical and numerical tools for solving dynamic economic problems; substantially revised for the second edition. This book offers a unified, comprehensive, and up-to-date treatment of analytical and numerical tools for solving dynamic economic problems. The focus is on introducing recursive methods—an important part of every economist's set of tools—and readers will learn to apply recursive methods to a variety of dynamic economic problems. The book is notable for its combination of theoretical foundations and numerical methods. Each topic is first described in theoretical terms, with explicit definitions and rigorous proofs; numerical methods and computer codes to implement these methods follow. Drawing on the latest research, the book covers such cutting-edge topics as asset price bubbles, recursive utility, robust control, policy analysis in dynamic New Keynesian models with the zero lower bound on interest rates, and Bayesian estimation of dynamic stochastic general equilibrium (DSGE) models. This second edition has been substantially updated. Responding to renewed interest in modeling with multiple equilibria, it incorporates new material on this topic throughout. It offers an entirely new chapter on deterministic nonlinear systems, and provides new material on such topics as linear planar systems, chaos, bifurcations, indeterminacy and sunspot solutions, pruning nonlinear solutions, the bandit problem, rational inattention models, bequests, self-fulfilling prophecies, the cyclical behavior of unemployment and vacancies, and the long-run risk model. The exposition of each chapter has been revised and improved, and many new figures, Matlab codes, and exercises have been added. A student solutions manual can be purchased separately.

The second edition of a rigorous and example-driven introduction to topics in economic dynamics that emphasizes techniques for modeling dynamic systems. This text provides an introduction to the modern theory of economic dynamics, with emphasis on mathematical and computational techniques for modeling dynamic systems. Written to be both rigorous and engaging, the book shows how sound understanding of the underlying theory leads to effective algorithms for solving real-world problems. The material makes extensive use of programming examples to illustrate ideas, bringing to life the abstract concepts in the text. Key topics include algorithms and scientific computing, simulation, Markov models, and dynamic programming. Part I introduces fundamentals and part II covers more advanced material. This second edition has been thoroughly updated, drawing on recent research in the field. New for the second edition: “Programming-language agnostic” presentation using pseudocode. New chapter 1 covering conceptual issues concerning Markov chains such as ergodicity and stability. New focus in chapter 2 on algorithms and techniques for program design and high-performance computing. New focus on household problems rather than optimal growth in material on dynamic programming. Solutions to many exercises, code, and other resources available on a supplementary website.

This book contains a concise description of important mathematical methods of dynamics and suitable economic models. It covers discrete as well as continuous-time systems, linear and nonlinear models. Mixing traditional and modern materials, the study covers dynamics with and without optimization, naive and rational expectations, respectively. In addition to standard models of growth and cycles, the book also contains original studies on control of a multisector economy and expectations-driven multicohort economy. Numerous examples, problems (with solutions) and figures complete the book.

An introduction to economic applications of the theory of continuous-time finance that strikes a balance between mathematical rigor and economic interpretation of financial market regularities. This book introduces the economic applications of the theory of continuous-time finance, with the goal of enabling the construction of realistic models, particularly those involving incomplete markets. Indeed, most recent applications of continuous-time finance aim to capture the imperfections and dysfunctions of financial markets—characteristics that became especially apparent during the market turmoil that started in 2008. The book begins by using discrete time to illustrate the basic mechanisms and introduce such notions as completeness, redundant pricing, and no arbitrage. It develops the continuous-time analog of those mechanisms and introduces the powerful tools of stochastic calculus. Going beyond other textbooks, the book then focuses on the study of markets in which some form of incompleteness, volatility, heterogeneity, friction, or behavioral subtlety arises. After presenting solutions methods for control problems and related partial differential equations, the text examines portfolio optimization and equilibrium in incomplete markets, interest rate and fixed-income modeling, and stochastic volatility. Finally, it presents models where investors form different beliefs or suffer frictions, form habits, or have recursive utilities, studying the effects not only on optimal portfolio choices but also on equilibrium, or the price of primitive securities. The book strikes a balance between mathematical rigor and the need for economic interpretation of financial market regularities, although with an emphasis on the latter.

Most financial and investment decisions are based on considerations of possible future changes and require forecasts on the evolution of the financial world. Time series and processes are the natural tools for describing the dynamic behavior of financial data, leading to the required forecasts. This book presents a survey of the empirical properties of financial time series, their descriptions by means of mathematical processes, and some implications for important financial applications used in many areas like risk evaluation, option pricing or portfolio construction. The statistical tools used to extract information from raw data are introduced. Extensive multiscale empirical statistics provide a solid benchmark of stylized facts (heteroskedasticity, long memory, fat-tails, leverage...), in order to assess various mathematical structures that can capture the observed regularities. The author introduces a broad range of processes and evaluates them systematically against the benchmark, summarizing the successes and limitations of these models from an empirical point of view. The outcome is that only multiscale ARCH processes with long memory, discrete multiplicative structures and non-normal innovations are able to capture correctly the empirical properties. In particular, only a discrete time series framework allows to capture all the stylized facts in a process, whereas the stochastic calculus used in the continuum limit is too constraining. The present volume offers various applications and extensions for this class of processes including high-frequency volatility estimators, market risk evaluation, covariance estimation and multivariate extensions of the processes. The book discusses many practical implications and is addressed to practitioners and quants in the financial industry, as well as to academics, including graduate (Master or PhD level) students. The prerequisites are basic statistics and some elementary financial mathematics.

Dynamic Programming in Economics is an outgrowth of a course intended for students in the first year PhD program and for researchers in Macroeconomics Dynamics. It can be used by students and researchers in Mathematics as well as in Economics. The purpose of Dynamic Programming in Economics is twofold: (a) to provide a rigorous, but not too complicated, treatment of optimal growth models in infinite discrete time horizon, (b) to train the reader to the use of optimal growth models and hence to help him to go further in his research. We are convinced that there is a place for a book which stays somewhere between the "minimum tool kit" and specialized monographs leading to the frontiers of research on optimal growth.