Some recent developments in the mathematics of optimization, including the concepts of invexity and quasimax, have not previously been applied to models of economic growth, and to finance and investment. Their applications to these areas are shown in this book. Results are presented concerning when an optimal control model has a unique optimum, what happens when the usual convexity assumptions are weakened or absent, and stability to small disturbances of the model or its parameters. The book introduces a new computational package called SCOM, for solving optimal control problems on MATLAB.
Some recent developments in the mathematics of optimization, including the concepts of invexity and quasimax, have not yet been applied to models of economic growth, and to finance and investment. Their applications to these areas are shown in this book.
From the review:
Craven and Islam have produced an excellent survey of recent applications of optimization to economics (especially growth theory) and finance. The exposition is clear, with good notation and a judicious mix of rigor and heuristic argument. As a bonus, they present a new SCOM program to compute solutions to social choice models. This book will surely prove to be a boon to the student, especially those who wish to learn about optimal growth under different conditions and assumptions. The text covers a wide range of optimization models in economics and finance, including non-linear programming, dynamic optimization, stochastic control and dynamic vector optimization models. The models are applicable to decision making, forecasting, simulation, sensitivity analysis and planning.
Professor David W. K. Yeung
Director of the Center of Game Theory
Professor of Decision Sciences
Hong Kong Baptist University
Hong Kong
&
Managing Editor, International Game Theory Review.
"This book is an interesting and interdisciplinary survey of applications of optimization to special parts of economics (growth theory) and finance. ? the whole contents of this book is presented in a unified manner. It is a pleasure to read the explicitly given hints to proposed extensions of existing methods and also to read discussions, assessments, recommendations and conclusions of the authors ? ." (Alfred Göpfert, Zentralblatt MATH, Vol. 1086, 2006)
"This book is concerned with the description of some basic and also advanced models in mathematical programming and optimal control and with some applications of these models to quantitative welfare economics and finance. ? This book is ? suitable as a reference book for researchers, academics, and doctoral students in the area of mathematical programming, finance and economics." (Giorgio Giorgi, Mathematical Reviews, Issue 2006 e)
