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.

Autorentext

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.

Zusammenfassung

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.

Inhalt
: Optimal Models for Economics and Finance.- Mathematics of Optimal Control.- Computing Optimal Control : The SCOM package.- Computing Optimal Growth and Development Models.- Modelling Financial Investment with Growth.- Modelling Sustainable Development.- Modelling and Computing a Stochastic Growth Model.- Optimization in Welfare Economics.- Transversality Conditions for Infinite Horizon.- Conclusions.