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.
Table of Contents
1. The genuine savings criterion and the value of population in an economy with endogenous fertility rate Kenneth J. Arrow, Alain Bensoussan, Qi Feng, and Suresh P. Sethi 2. Continuous time overlapping generations models Hippolyte d'Albis and Emmanuelle Augeraud-Véron 3. Modeling technological change in equipment replacement problems Chin Hon Tan and Joseph C. Hartman 4. Embodied technology adoption under uncertainty Bruno Cruz and Aude Pommeret 5. Viability, optimality, and sustainability in vintage models Noël Bonneuil 6. Embodied technical change and learning-by-doing in a two sector growth model with human capital accumulation Alberto Bucci, Herb Kunze and Davide La Torre 7. Age-structured optimization models in fisheries bioeconomics: a survey Olli Tahvonen 8. Age-structured models and optimal control in mathematical epidemiology: a survey David Greenhalgh 9. Optimal management of a size distributed forest with respect to timber and non-timber values Renan-Ulrich Goertz and Angels Xabadia 10. Optimal harvesting in a two-species model of size-structured population Nobuyuki Kato 11. Optimisation problems in the management of indigenous plant populations under grazing pressure Lynne McArthur, John Boland, and Fleur Tiver 12. Identification of age-structured contamination sources in ground water Sergey Lyashko, Dmitry Klyushin, Dmitry Nomirovsky, and Vladimir Semenov
Raouf Boucekkine is Professor of Economics at the Catholic University of Louvain, Belgium, and the University of Glasgow, UK. He is currently research co-director of the Center of Operation Research and Econometrics (CORE) at Louvain-la-Neuve, Belgium.
Natali Hritonenko is a Professor in the Department of Mathematics at Prairie View A&M University, USA.
Yuri Yatsenko is a Professor in the School of Business at Houston Baptist University, USA.