Optimization In Economics And Finance,9780387242798

Optimization In Economics And Finance

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ISBN13: 9780387242798
ISBN10: 0387242791
Format: Hardcover
Pub. Date: 2005-08-01
Publisher(s): Springer Verlag
List Price: $179.99

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Summary

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.

Author Biography

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.

Table of Contents

Preface ix
Acknowledgements and Sources of Materials xi
Chapter One: Introduction: Optimal Models for Economics and Finance 1(8)
1.1 Introduction
1(1)
1.2 Welfare economics and social choice: modelling and applications
2(3)
1.3 The objectives of this book
5(1)
1.4 An example of an optimal control model
6(1)
1.5 The structure of the book
7(2)
Chapter Two: Mathematics of Optimal Control 9(26)
2.1 Optimization and optimal control models
9(3)
2.2 Outline of the Pontryagin Theory
12(2)
2.3 When is an optimum reached?
14(2)
2.4 Relaxing the convex assumptions
16(2)
2.5 Can there be several optima?
18(2)
2.6 Jump behaviour with a pseudoconcave objective
20(4)
2.7 Generalized duality
24(5)
2.8 Multiobjective (Pareto) optimization
29(1)
2.9 Multiobjective optimal control
30(2)
2.10 Multiobjective Pontryagin conditions
32(3)
Chapter Three: Computing Optimal Control: The SCOM package 35(20)
3.1 Formulation and computational approach
35(2)
3.2 Computational requirements
37(3)
3.3 Using the SCOM package
40(1)
3.4 Detailed account of the SCOM package
41(5)
3.4.1 Preamble
41(1)
3.4.2 Format of problem
41(1)
3.4.3 The SCOM codes: The user does not alter them
42(4)
3.5 Functions for the first test problem
46(1)
3.6 The second test problem
47(2)
3.7 The third test problem
49(6)
Chapter Four: Computing Optimal Growth and Development Models 55(11)
4.1 Introduction
55(1)
4.2 The Kendrick-Taylor growth model
56(1)
4.3 The Kendrick-Taylor model implementation
57(3)
4.4 Mathematical and economic properties of the results
60(4)
4.5 Computation by other computer programs
64(1)
4.6 Conclusions
64(2)
Chapter Five: Modelling Financial Investment with Growth 66(18)
5.1 Introduction
66(1)
5.2 Some related literature
66(3)
5.3 Some approaches
69(1)
5.4 A proposed model for interaction between investment and physical capital
70(2)
5.5 A computed model with small stochastic term
72(3)
5.6 Multiple steady states in a dynamic financial model
75(5)
5.7 Sensitivity questions concerning infinite horizons
80(1)
5.8 Some conclusions
81(1)
5.9 The MATLAB codes
82(1)
5.10 The continuity required for stability
83(1)
Chapter Six: Modelling Sustainable Development 84(27)
6.1 Introduction
84(1)
6.2 Welfare measures and models for sustainability
84(3)
6.3 Modelling sustainability
87(5)
6.3.1 Description by objective function with parameters
87(2)
6.3.2 Modified discounting for long-term modelling
89(1)
6.3.3 Infinite horizon model
90(2)
6.4 Approaches that might be computed
92(4)
6.4.1 Computing for a large time horizon
92(1)
6.4.2 The Chichilnisky compared with penalty term model
92(2)
6.4.3 Chichilnisky model compared with penalty model
94(1)
6.4.4 Pareto optimum and intergenerational equality
95(1)
6.4.5 Computing with a modified discount factor
95(1)
6.5 Computation of the Kendrick-Taylor model
96(3)
6.5.1 The Kendrick-Taylor model
96(1)
6.5.2 Extending the Kendrick-Taylor model to include a long time horizon
97(1)
6.5.3 Chichilnisky variant of Kendrick-Taylor model
98(1)
6.5.4 Transformation of the Kendrick-Taylor model
98(1)
6.6 Computer packages and results of computation of models
99(9)
6.6.1 Packages used
99(1)
6.6.2 Results: comparison of the basic model solution with results for modified discount factor
99(2)
6.6.3 Results: effect of increasing the horizon T
101(2)
6.6.4 Results: Effect of omitting the growth term in the dynamic equation
103(1)
6.6.5 Results: parametric approach
103(2)
6.6.6 Results: the modified Chichilnisky approach
105(3)
6.7 Existence, uniqueness and global optimization
108(1)
6.8 Conclusions
109(1)
6.9 User programs for transformed Kendrick-Taylor model for sustainable growth
110(1)
Chapter Seven: Modelling and Computing a Stochastic Growth Model 111(12)
7.1 Introduction
112(1)
7.2 Modelling stochastic growth
112(1)
7.3 Calculating mean and variance
113(1)
7.4 Computed results for stochastic growth
114(2)
7.5 Requirements for RIOTS_95 as M-files
116(7)
Chapter Eight: Optimization in Welfare Economics 123(8)
8.1 Static and dynamic optimization
123(1)
8.2 Some static welfare models
123(2)
8.3 Perturbations and stability
125(1)
8.4 Some multiobjective optimal control models
126(2)
8.5 Computing multiobjective optima
128(1)
8.6 Some conditions for invexity
129(1)
8.7 Discussion
130(1)
Chapter 9: Transversality Conditions for Infinite Horizon Models 131(16)
9.1 Introduction
131(1)
9.2 Critical literature survey and extensions
131(4)
9.3 Standard optimal control model
135(1)
9.4. Gradient conditions for transversality
136(3)
9.5 The model with infinite horizon
139(1)
9.6 Normalizing a growth model with infinite horizon models
139(2)
9.7 Shadow prices
141(1)
9.8 Sufficiency conditions
142(1)
9.9 Computational approaches for infinite horizon
143(3)
9.10 Optimal control models in finance: special considerations
146(1)
9.11 Conclusions
146(1)
Chapter 10: Conclusions 147(2)
Bibliography 149(9)
Index 158

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