© 2005

Optimization in Economics and Finance

Some Advances in Non-Linear, Dynamic, Multi-Criteria and Stochastic Models

  • 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

  • Some 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

  • A new computational package called SCOM, for solving optimal control problems on MATLAB, is introduced. It facilitates computational experiments, in which there are changes to model features or parameters


Part of the Dynamic Modeling and Econometrics in Economics and Finance book series (DMEF, volume 7)

About this book


Many optimization questions arise in economics and finance; an important example of this is the society's choice of the optimum state of the economy (the social choice problem). Optimization in Economics and Finance extends and improves the usual optimization techniques, in a form that may be adopted for modeling social choice problems. Problems discussed include: when is an optimum reached; when is it unique; relaxation of the conventional convex (or concave) assumptions on an economic model; associated mathematical concepts such as invex and quasimax; multiobjective optimal control models; and related computational methods and programs. These techniques are applied to economic growth models (including small stochastic perturbations), finance and financial investment models (and the interaction between financial and production variables), modeling sustainability over long time horizons, boundary (transversality) conditions, and models with several conflicting objectives. Although the applications are general and illustrative, the models in this book provide examples of possible models for a society's social choice for an allocation that maximizes welfare and utilization of resources. As well as using existing computer programs for optimization of models, a new computer program, named SCOM, is presented in this book for computing social choice models by optimal control.


Decision Finance Investment Making Modelling Paraplusig Stochastic model Stochastic models economic growth growth growth model modeling optimization

Authors and affiliations

  1. 1.University of MelbourneAustralia
  2. 2.Victoria UniversityMelbourneAustralia

About the authors

Dr. B. D. Craven was (until retirement) a Reader in Mathematics at University of Melbourne, Australia, where he taught Mathematics and various topics in Operations Research for over 35 years. He holds a D.Sc. degree from University of Melbourne. His research interests include continuous optimization, nonlinear and multiobjective optimization, and optimal control. and their applcations. He has published five books, including two on mathematical programming and optimal control, and many papers in international journals. He is a member of Australian Society for Operations Research and INFORMS.

Prof. Sardar M N Islam is Professor of Welfare and Environmental Economics at Victoria University, Australia. He is also associated with the Financial Modelling Program, and the Law and Economics Program there. He has published 11 books and monographs and more than 150 technical papers in Economics (Mathematical Economics, Applied Welfare Economics, Optimal Growth), Corporate Governance, Mathematical Finance, Financial Econometrics and E-Commerce.

Bibliographic information


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)