Bjarne S. Jensen – författare

Two central problems in the pure theory of economic growth are analysed in this monograph: 1) the dynamic laws governing the economic growth processes, 2) the kinematic and geometric properties of the set of solutions to the dynamic systems. With allegiance to rigor and the emphasis on the theoretical fundamentals of prototype mathematical growth models, the treatise is written in the theorem-proof style. To keep the exposition orderly and as smooth as possible, the economic analysis has been separated from the purely mathematical issues, and hence the monograph is organized in two books. Regarding the scope and content of the two books, an "Introduction and Over­ view" has been prepared to offer both motivation and a brief account. The introduc­ tion is especially designed to give a recapitulation of the mathematical theory and results presented in Book II, which are used as the unifying mathematical framework in the analysis and exposition of the different economic growth models in Book I. Economists would probably prefer to go directly to Book I and proceed by consult­ ing the mathematical theorems of Book II in confirming the economic theorems in Book I. Thereby, both the independence and interdependence of the economic and mathematical argumentations are respected.

This updated and expanded book examines the fundamentals of economic growth models as expressed by dynamic systems of nonlinear differential equations. With homogeneous dynamic systems as the unifying mathematical framework, the time paths and long-run stability properties of the solutions to classical, neoclassical, and modern macroeconomic growth models are analyzed. The general structure and solutions of two-sector and multi-sector growth models are also explored, with special attention given to the evolution of output compositions and sectoral factor allocations involved in Walrasian general equilibrium dynamics. Ramsey optimal growth (saving) models with variable intertemporal substitution (non-homothetic utility) are discussed to demonstrate the ability to generate a realistic historically observed evolution of economic per capita growth rates and saving rates. The book aims to highlight how basic economic growth models can be extended widely, including international trading economies, world market prices, commodity trade patterns, and issues related to globalization, migrations, and international factor movements. It will be relevant to students and researchers interested in economic growth and trade policy.

This updated and expanded book examines the fundamentals of economic growth models as expressed by dynamic systems of nonlinear differential equations. With homogeneous dynamic systems as the unifying mathematical framework, the time paths and long-run stability properties of the solutions to classical, neoclassical, and modern macroeconomic growth models are analyzed. The general structure and solutions of two-sector and multi-sector growth models are also explored, with special attention given to the evolution of output compositions and sectoral factor allocations involved in Walrasian general equilibrium dynamics. Ramsey optimal growth (saving) models with variable intertemporal substitution (non-homothetic utility) are discussed to demonstrate the ability to generate a realistic historically observed evolution of economic per capita growth rates and saving rates. The book aims to highlight how basic economic growth models can be extended widely, including international trading economies, world market prices, commodity trade patterns, and issues related to globalization, migrations, and international factor movements. It will be relevant to students and researchers interested in economic growth and trade policy.

This book analyses stochastic dynamic systems across a broad spectrum in economics and finance. The major unifying theme is the coherent and rigorous treatment of uncertainty and its implications for describing stochastic processes by the stochastic differential equations of the fundamental models in various fields. Pertinent subjects are interrelated, juxtaposed, and examined for consistency in theoretical and empirical contexts. The volume consists of three parts: Developments in Stochastic Dynamics; Stochastic Dynamics in Basic Economic Growth Models; Intertemporal Optimisation in Consumption, Finance, and Growth. Key topics include: fractional Brownian motion in finance; moment evolution of Gaussian and geometric Wiener diffusions; stochastic kinematics and stochastic mechanics; stochastic growth in continuous time; time delays and Hopf bifurcation; consumption and investment strategies; differential systems in finance and life insurance; uncertainty of technological innovations; investment and employment cycles; stochastic control theory; and risk aversion. The works collected in this book serves to bridge the "old" deterministic dynamics and the "new" stochastic dynamics. The collection is important for scholars and advanced graduate students of economics, statistics, and applied mathematics.

Two central problems in the pure theory of economic growth are analysed in this monograph: 1) the dynamic laws governing the economic growth processes, 2) the kinematic and geometric properties of the set of solutions to the dynamic systems. With allegiance to rigor and the emphasis on the theoretical fundamentals of prototype mathematical growth models, the treatise is written in the theorem-proof style. To keep the exposition orderly and as smooth as possible, the economic analysis has been separated from the purely mathematical issues, and hence the monograph is organized in two books. Regarding the scope and content of the two books, an "Introduction and Over­ view" has been prepared to offer both motivation and a brief account. The introduc­ tion is especially designed to give a recapitulation of the mathematical theory and results presented in Book II, which are used as the unifying mathematical framework in the analysis and exposition of the different economic growth models in Book I. Economists would probably prefer to go directly to Book I and proceed by consult­ ing the mathematical theorems of Book II in confirming the economic theorems in Book I. Thereby, both the independence and interdependence of the economic and mathematical argumentations are respected.