Rose-Anne Dana - Böcker

This book 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 this book is twofold: to provide a rigorous, but not too complicated, treatment of optimal growth models in infinite discrete time horizon; and to train the reader to use optimal growth models and hence to help him to go further in his research.

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.

The problem of e?cient or optimal allocation of resources is a fundamental concern of economic analysis. The theory of optimal economic growth can be viewedasanaspectofthiscentraltheme,whichemphasizesingeneraltheissues arising in the allocation of resources over an in?nite time horizon, and in p- ticular the consumption-investment decision process in models in which there is no natural ”terminal date”. This broad scope of ”optimal growth theory” is one which has evolved over time, as economists have discovered new interp- tations of its central results, as well as new applications of its basic methods. The purpose of this handbook is to provide surveys of some signi?cant results of the theory of optimal growth,as well as the techniques of dynamic optimi- tion theory on which they are based. Armed with the results and methods of this theory, a researcher should be in an advantageous position to apply these versatile methods of analysis to new issues in the area of dynamic economics, as well as to contribute to the further development of the mathematical te- niques of optimization over time. The survey included in this volume all have as a common starting point the seminal contribution of Frank Ramsey (1928).

In modern financial practice, asset prices are modelled by means of stochastic processes, and continuous-time stochastic calculus thus plays a central role in financial modelling. This approach has its roots in the foundational work of the Nobel laureates Black, Scholes and Merton. Asset prices are further assumed to be rationalizable, that is, determined by equality of demand and supply on some market. This approach has its roots in the foundational work on General Equilibrium of the Nobel laureates Arrow and Debreu and in the work of McKenzie. This book has four parts. The first brings together a number of results from discrete-time models. The second develops stochastic continuous-time models for the valuation of financial assets (the Black-Scholes formula and its extensions), for optimal portfolio and consumption choice, and for obtaining the yield curve and pricing interest rate products. The third part recalls some concepts and results of general equilibrium theory, and applies this in financial markets. The last part is more advanced and tackles market incompleteness and the valuation of exotic options in a complete market.

In modern financial practice, asset prices are modelled by means of stochastic processes, and continuous-time stochastic calculus thus plays a central role in financial modelling. This approach has its roots in the foundational work of the Nobel laureates Black, Scholes and Merton. Asset prices are further assumed to be rationalizable, that is, determined by equality of demand and supply on some market. This approach has its roots in the foundational work on General Equilibrium of the Nobel laureates Arrow and Debreu and in the work of McKenzie. This book has four parts. The first brings together a number of results from discrete-time models. The second develops stochastic continuous-time models for the valuation of financial assets (the Black-Scholes formula and its extensions), for optimal portfolio and consumption choice, and for obtaining the yield curve and pricing interest rate products. The third part recalls some concepts and results of general equilibrium theory, and applies this in financial markets. The last part is more advanced and tackles market incompleteness and the valuation of exotic options in a complete market.