发帖
雷达卡
274013.pdf
(5.63 MB, 需要: 10 个论坛币)
List of Figures
List of Tables
Preface
Introduction
ix
xi
xiii
xv
1. OPTIMAL CONTROL MODELS
1
2
3
4
5
6
7
8
An Optimal Control Model of Finance
(Karush) Kuhn-Tucker Condition
Pontryagin Theorem
Bang-Bang Control
Singular Arc
Indifference Principle
Different Approaches to Optimal Control Problems
Conclusion
1
2
4
6
7
7
8
10
20
2. THE STV APPROACH TO FINANCIAL OPTIMAL CONTROL
MODELS
1
2
3
4
5
6
7
Introduction
Piecewise-linear Transformation
Non-linear Time Scale Transformation
A Computer Software Package Used in this Study
An Optimal Control Problem When the Control can only Take
the Value 0 or 1
Approaches to Bang-Bang Optimal Control with a Cost of
Changing Control
An Investment Planning Model and Results
21
21
21
23
25
26
27
30
vi OPTIMAL CONTROL MODELS IN FINANCE
8 Financial Implications and Conclusion 36
3. A FINANCIAL OSCILLATOR MODEL
1
2
3
4
5
6
7
Introduction
Controlling a Damped Oscillator in a Financial Model
Oscillator Transformation of the Financial Model
Computational Algorithm: The Steps
Financial Control Pattern
Computing the Financial Model: Results and Analysis
Financial Investment Implications and Conclusion
39
39
40
41
44
47
47
89
4. AN OPTIMAL CORPORATE FINANCING MODEL
1
2
3
4
5
6
7
8
9
Introduction
Problem Description
Analytical Solution
Penalty Terms
Transformations for the Computer Software Package for the
Finance Model
Computational Algorithms for the Non-linear Optimal Control
Problem
Computing Results and Conclusion
Optimal Financing Implications
Conclusion
91
91
91
94
98
99
101
104
107
108
5. FURTHER COMPUTATIONAL EXPERIMENTS AND RESULTS
1
2
3
4
Introduction
Different Fitting Functions
The Financial Oscillator Model when the Control Takes Three
Values
Conclusion
109
109
109
120
139
6. CONCLUSION 141
Appendices 145
A CSTVA Program List 145
1
2
3
4
Program A: Investment Model in Chapter 2
Program B: Financial Oscillator Model in Chapter 3
Program C: Optimal Financing Model in Chapter 4
Program D: Three Value-Control Model in Chapter 5
145
149
153
156
Contents vii
B Some Computation Results
1
2
3
4
Results for Program A
Results for Program B
Results for Program C
Results for Program D
C
D
E
F
Differential Equation Solver from the SCOM Package
SCOM Package
Format of Problem Optimization
A Sample Test Problem
161
161
163
167
175
181
183
189
191
References
Index
193
199
京公网安备 11010802022788号
