Adaptive Processes in Economic Systems - 1st Edition - ISBN: 9781483230177, 9781483264073

Adaptive Processes in Economic Systems

1st Edition

Authors: Roy E. Murphy
Editors: Richard Bellman
eBook ISBN: 9781483264073
Imprint: Academic Press
Published Date: 1st January 1965
Page Count: 224
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Description

Mathematics in Science and Engineering, Volume 20, Adaptive Processes in Economic Systems demonstrates the usefulness of communications theory, self-adaptive control theory, and thermodynamic theory to certain economic processes.

This book discusses the common properties of adaptive processes, role of the decision maker, and mixed adaptive processes of the first and second kind. The economic environmental processes, concept of entropy time, and stochastic dynamic economic process are also elaborated. This text likewise covers the investment model with full liquidity, adaptive capital allocation process, and concept of an economic state space. Other topics include the stochastic equilibrium in the market and individual adaptive behavior.

This volume is suitable for engineers, economists, and specialists of disciplines related to economic systems.

Table of Contents


Preface

Chapter 1 Introduction

1.1 The Historical and Current Development of Adaptive Theory

1.2 Common Properties of Adaptive Processes

References

Chapter 2 The Mathennatical Model

2.1 Introduction

2.2 Discrete Processes

2.3 Some Discrete Sequential Processes

2.4 The Role of the Decision Maker

2.5 The Optimal Type 2 (Adaptive) Process

2.6 The Constrained, Optimal Type 2 (Adaptive) Process

2.7 Causality and Markov Processes

2.8 The Dynamic Programming Model

References

Chapter 3 The Primitive Adaptive Process

3.1 The Notion of Learning and Adaptation

3.2 Some Hypothetical Experiments

3.3 An Adaptive Process of the First Kind

3.4 An Adaptive Process of the Second Kind

3.5 Mixed Adaptive Processes of the First and Second Kind

3.6 Summary

References

Chapter 4 Subjective Probability

4.1 Introduction

4.2 A Heuristic Example—The Three Investors

4.3 Economic Environmental Processes

4.4 A Digression on Statistical Estimators

4.5 Multinomial Subjective Probabilities

4.6 Properties of the Subjective Probability Vector

References

Chapter 5 The Role of Entropy in Economic Processes

5.1 The Concept of Entropy Time

5.2 Entropy and Information

5.3 The Entropy Paradox

References

Chapter 6 Adaptive Economic Processes

6.1 Introduction

6.2 General Deterministic Dynamic Economic Process

6.3 The Stochastic Dynamic Economic Process

6.4 The Adaptive Stochastic Dynamic Economic Process

6.5 Stochastic Growth Process

Chapter 7 An Adaptive Investment Model

7.1 The Objective Function

7.2 An Example—The Three Investors Again

7.3 An Investment Model with Full Liquidity

7.4 An Adaptive Investment Process with Full Liquidity

7.5 Consideration of the Special Constraint

7.6 The Multivalued Payoff Adaptive Investment Process

Chapter 8 Multiactivity Capital Allocation Processes

8.1 Introduction

8.2 The Adaptive Capital Allocation Process

8.3 The Properties of the Adaptive Capital Allocation Process in the Limit

References

Chapter 9 Economic State Space

9.1 Introduction

9.2 The Concept of an Economic State Space

9.3 Statistical Equilibrium and Enlightenment

9.4 The Subjective Entropy Trajectory

9.5 The Dynamics of the Subjective Entropy Trajectory

9.6 The Economic State Space Representation

9.7 A Digression—^A Likely Value for the Environmental Entropy

References

Chapter 10 Interactions Between Decision Makers in State Space

10.1 Introduction

10.2 The State Space Probability Function

10.3 Stochastic Equilibrium in the Market

10.4 Interperson Trading in the Investment Market

Chapter 11 The Conclusions

11.1 Individual Adaptive Behavior

11.2 Collective Adaptive Behavior

Bibliography

1. General Background on Adaptive and Evolutionary Behavior

2. Sources on the Concept of Subjective Probability

3. Sources on the Mathematical Theory of Intelligence

4. Dynamic Programming and Adaptive Control

5. Sources on Investment Theory; mainly on Multi-Project Investment Under Uncertainty

6. Sources on Information Theory

7. Sources on the Concept of Entropy and Entropy-Gradient

8. Sources on Statistical Mechanics and Thermodynamics

9. Sources on Certain Techniques Used in This Book

Subject Index

Details

No. of pages:
224
Language:
English
Copyright:
© Academic Press 1965
Published:
Imprint:
Academic Press
eBook ISBN:
9781483264073

About the Author

Roy E. Murphy

Affiliations and Expertise

DEPARTMENT OF ECONOMICS STANFORD UNIVERSITY STANFORD, CALIFORNIA

About the Editor

Richard Bellman

Affiliations and Expertise

Departments of Mathematics, Electrical Engineering, and Medicine University of Southern California Los Angeles, California