Download or read book Dynamic Programming Maximum Principle and Vintage Capital written by Giorgio Fabbri and published by . This book was released on 2007 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present an application of the Dynamic Programming (DP) and of the Maximum Principle (MP) to solve an optimization over time when the production function is linear in the stock of capital (Ak model). Two views of capital are considered. In one, which is embraced by the great majority of macroeconomic models, capital is homogenous and depreciates at a constant exogenous rate. In the other view each piece of capital has its own amp;finite productive life cycle (vintage capital). The interpretation of the time patterns of macroaggregates is quite different betweeen the two cases. A technological shock generates an oscillatory movement in the time pattern of per capita output when capital has a vintage structure; conversely an instantaneous adjustment with no transitional dynamics occurs when capital is homogenous.From a methodological point of view it emerges that the DP approach delivers sharper results than the MP approach (for instance it delivers a closed form solution for the optimal investment strategy) under slacker parameter restrictions.Cross-time and cross-country data on investments, income, and consumption drawn from the Penn World Table version 6.2 are used to evaluate the vintage and standard Ak model.
Download or read book Vintage Capital in the AK Growth Model written by Giorgio Fabbri and published by . This book was released on 2008 with total page 49 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper deals with an endogenous growth model with vintage capital and, more precisely, with the AK model proposed in [18]. In endogenous growth models the introduction of vintage capital allows to explain some growth facts but strongly increases the mathematical diamp;fficulties. So far, in this approach, the model is studied by the Maximum Principle; here we develop the Dynamic Programming approach to the same problem by obtaining sharper results and we provide more insight about the economic implications of the model. We explicitly amp;find the value function, the closed loop formula that relates capital and investment, the optimal consumption paths and the long run equilibrium. The short run amp;fluctuations of capital and investment andthe relations with the standard AK model are analyzed. Finally the applicability to other models s also discussed.
Download or read book Solving Optimal Growth Models with Vintage Capital the Dynamic Programming Approach written by and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper deals with an endogenous growth model with vintage capital and, more precisely, with the AK model proposed in [R. Boucekkine, O. Licandro, L.A. Puch, F. del Rio, Vintage capital and the dynamics of the AK model, J. Econ. Theory 120 (1) (2005) 39-72]. In endogenous growth models the introduction of vintage capital allows to explain some growth facts but strongly increases the mathematical difficulties. So far, in this approach, the model is studied by the Maximum Principle; here we develop the Dynamic Programming approach to the same problem by obtaining sharper results and we provide more insight about the economic implications of the model. We explicitly find the value function, the closed loop formula that relates capital and investment, the optimal consumption paths and the long run equilibrium. The short run fluctuations of capital and investment and the relations with the standard AK model are analyzed. Finally the applicability to other models is also discussed.
Download or read book Stochastic Optimal Control in Infinite Dimension written by Giorgio Fabbri and published by Springer. This book was released on 2017-06-22 with total page 928 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing an introduction to stochastic optimal control in infinite dimension, this book gives a complete account of the theory of second-order HJB equations in infinite-dimensional Hilbert spaces, focusing on its applicability to associated stochastic optimal control problems. It features a general introduction to optimal stochastic control, including basic results (e.g. the dynamic programming principle) with proofs, and provides examples of applications. A complete and up-to-date exposition of the existing theory of viscosity solutions and regular solutions of second-order HJB equations in Hilbert spaces is given, together with an extensive survey of other methods, with a full bibliography. In particular, Chapter 6, written by M. Fuhrman and G. Tessitore, surveys the theory of regular solutions of HJB equations arising in infinite-dimensional stochastic control, via BSDEs. The book is of interest to both pure and applied researchers working in the control theory of stochastic PDEs, and in PDEs in infinite dimension. Readers from other fields who want to learn the basic theory will also find it useful. The prerequisites are: standard functional analysis, the theory of semigroups of operators and its use in the study of PDEs, some knowledge of the dynamic programming approach to stochastic optimal control problems in finite dimension, and the basics of stochastic analysis and stochastic equations in infinite-dimensional spaces.
Download or read book Optimal Control of Nonlinear Processes written by Dieter Grass and published by Springer Science & Business Media. This book was released on 2008-07-24 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dynamic optimization is rocket science – and more. This volume teaches researchers and students alike to harness the modern theory of dynamic optimization to solve practical problems. These problems not only cover those in space flight, but also in emerging social applications such as the control of drugs, corruption, and terror. This volume is designed to be a lively introduction to the mathematics and a bridge to these hot topics in the economics of crime for current scholars. The authors celebrate Pontryagin’s Maximum Principle – that crowning intellectual achievement of human understanding. The rich theory explored here is complemented by numerical methods available through a companion web site.
Download or read book Mathematical Modeling in Economics Ecology and the Environment written by Natali Hritonenko and published by Springer Science & Business Media. This book was released on 2014-01-08 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: Updated to textbook form by popular demand, this second edition discusses diverse mathematical models used in economics, ecology, and the environmental sciences with emphasis on control and optimization. It is intended for graduate and upper-undergraduate course use, however, applied mathematicians, industry practitioners, and a vast number of interdisciplinary academics will find the presentation highly useful. Core topics of this text are: · Economic growth and technological development · Population dynamics and human impact on the environment · Resource extraction and scarcity · Air and water contamination · Rational management of the economy and environment · Climate change and global dynamics The step-by-step approach taken is problem-based and easy to follow. The authors aptly demonstrate that the same models may be used to describe different economic and environmental processes and that similar investigation techniques are applicable to analyze various models. Instructors will appreciate the substantial flexibility that this text allows while designing their own syllabus. Chapters are essentially self-contained and may be covered in full, in part, and in any order. Appropriate one- and two-semester courses include, but are not limited to, Applied Mathematical Modeling, Mathematical Methods in Economics and Environment, Models of Biological Systems, Applied Optimization Models, and Environmental Models. Prerequisites for the courses are Calculus and, preferably, Differential Equations.
Download or read book Optimal Control of Age structured Populations in Economy Demography and the Environment written by Raouf Boucekkine and published by Routledge. This book was released on 2013-05-13 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers a wide range of topics within mathematical modelling and the optimization of economic, demographic, technological and environmental phenomena. Each chapter is written by experts in their field and represents new advances in modelling theory and practice. These essays are exemplary of the fruitful interaction between theory and practice when exploring global and local changes. The unifying theme of the book is the use of mathematical models and optimization methods to describe age-structured populations in economy, demography, technological change, and the environment. Emphasis is placed on deterministic dynamic models that take age or size structures, delay effects, and non-standard decision variables into account. In addition, the contributions deal with the age structure of assets, resources, and populations under study. Interdisciplinary modelling has enormous potential for discovering new insights in global and regional development. Optimal Control of Age-structured Populations in Economy, Demography, and the Environment is a rich and excellent source of information on state-of-the-art modelling expertise and references. The book provides the necessary mathematical background for readers from different areas, such as applied sciences, management sciences and operations research, which helps guide the development of practical models. As well as this the book also surveys the current practice in applied modelling and looks at new research areas for a general mathematical audience. This book will be of interest primarily to researchers, postgraduate students, as well as a wider scientific community, including those focussing on the subjects of applied mathematics, environmental sciences, economics, demography, management, and operations research.
Download or read book SIAM Journal on Control and Optimization written by Society for Industrial and Applied Mathematics and published by . This book was released on 2009 with total page 1140 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Economics Advances in Research and Application 2011 Edition written by and published by ScholarlyEditions. This book was released on 2012-01-09 with total page 593 pages. Available in PDF, EPUB and Kindle. Book excerpt: Economics: Advances in Research and Application: 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Economics and Organizations. The editors have built Economics: Advances in Research and Application: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Economics and Organizations in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Economics: Advances in Research and Application: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
Download or read book Dynamic Programming and Pontryagin s Maximum Principle written by Hans Sagan and published by . This book was released on 1967 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Principles of Dynamic Programming Basic analytic and computational methods written by Robert Edward Larson and published by . This book was released on 1978 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Dynamic programming and Pontryagin s maximum principle written by Klaus Neumann and published by . This book was released on 1968 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Green Growth and Sustainable Development written by Jesús Crespo Cuaresma and published by Springer Science & Business Media. This book was released on 2012-12-21 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book examines problems associated with green growth and sustainable development on the basis of recent contributions in economics, natural sciences and applied mathematics, especially optimal control theory. Its main topics include pollution, biodiversity, exhaustible resources and climate change. The integrating framework of the book is dynamic systems theory which offers a common basis for multidisciplinatory research and mathematical tools for solving complicated models, leading to new insights in environmental issues.
Download or read book Dynamic Programming written by Douglas John White and published by . This book was released on 1969 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Dynamic Optimization Second Edition written by Morton I. Kamien and published by Courier Corporation. This book was released on 2013-04-17 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since its initial publication, this text has defined courses in dynamic optimization taught to economics and management science students. The two-part treatment covers the calculus of variations and optimal control. 1998 edition.
Download or read book Sequential Optimization written by Joseph Burstein and published by . This book was released on 1985 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Discrete and Continuous Dynamical Systems written by and published by . This book was released on 2005 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt:
