Complex-Valued Modeling in Economics and Finance （经济学中的复变函数）15金币

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xpanda 发表于 2013-9-18 10:34:18 |AI写论文

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Title：Complex-Valued Modeling in Economics and Finance
Author：Sergey Svetunkov
Publisher：Springer
Contents：
1 Theoretical Basis of Complex Economy . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Complex Economies as a New Branch of Economics
and Mathematical Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Basic Concepts of the TFCV . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3 Axiomatic Core of the Theory of the Complex Economy . . . . . . . 14
1.4 Basic Model of a Complex Economy . . . . . . . . . . . . . . . . . . . . . 16
1.5 Some Data on Minkowsky’s Geometry . . . . . . . . . . . . . . . . . . . . 21
1.6 Laplace Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2 Properties of Complex Numbers of a Real Argument
and Real Functions of a Complex Argument . . . . . . . . . . . . . . . . . . 27
2.1 General Problem of Conformal Mapping
in Complex-Valued Economics . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.2 Complex Functions of a Real Argument . . . . . . . . . . . . . . . . . . . 28
2.3 Functions of a Complex Argument: Linear Function . . . . . . . . . . 42
2.4 Power Function of a Complex Argument
with a Real Exponent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.5 Exponential Function of Complex Argument
with Imaginary Exponent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.6 Power Function of Complex Argument
with Complex Exponent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.7 Exponential Function of a Complex Argument . . . . . . . . . . . . . . . 55
2.8 Logarithmic Function of a Complex Argument . . . . . . . . . . . . . . 59
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3 Conformal Mappings of Functions of a Complex Variable . . . . . . . . 63
3.1 Power Functions of a Complex Variable . . . . . . . . . . . . . . . . . . . 63
3.2 Exponential Functions of Complex Variables . . . . . . . . . . . . . . . . 75
3.3 Logarithmic Functions of Complex Variables . . . . . . . . . . . . . . . 78
3.4 Zhukovsky’s Function and Trigonometric
Complex Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4 Principles of Complex-Valued Econometrics . . . . . . . . . . . . . . . . . . 87
4.1 Statistics of Random Complex Value:
Standard Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.2 Method of Least Squares of Complex Variables:
Standard Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
4.3 Correlation Analysis of Complex Variables:
Contradictions of the Standard Approach . . . . . . . . . . . . . . . . . . 95
4.4 Consistent Axioms of the Theory of Mathematical
Statistics of Random Complex Variables . . . . . . . . . . . . . . . . . . 101
4.5 Least-Squares Method from the Point of View
of the New Axiomatic Theory . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.6 Complex Pair Correlation Coefficient . . . . . . . . . . . . . . . . . . . . 112
4.7 Interpretation of Values of Complex Pair
Correlation Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
4.8 Assessments of Parameters of Nonlinear Econometric
Models of Complex Variables . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.9 Assessment of Confidence Limits of Selected Values
of Complex-Valued Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
4.10 Balancing Factor in Evaluating the Adequacy
of Econometric Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
5 Production Functions of Complex Argument . . . . . . . . . . . . . . . . . . 143
5.1 Fundamentals of Production Functions
of a Complex Argument . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
5.2 Linear Complex-Valued Model of a Complex
Argument and Multicollinearity . . . . . . . . . . . . . . . . . . . . . . . . . 146
5.3 Linear Production Function of a Complex Argument . . . . . . . . . 155
5.4 Power Production Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
5.5 Exponential Production Function of Complex Argument . . . . . . . 172
5.6 Logarithmic Production Function of Complex Argument . . . . . . 175
5.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
6 Production Functions of Complex Variables . . . . . . . . . . . . . . . . . . . 181
6.1 General Provisions of the Theory of Production
Functions with Complex Variables . . . . . . . . . . . . . . . . . . . . . . . 181
6.2 Linear Production Function of Complex Variables . . . . . . . . . . . . 185
6.3 Model of Power Production Function of Complex
Variables with Real Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . 194
6.4 Power Production Complex-Valued Functions
with Real Coefficients of the Diatom Plant
and Russian Industry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
6.5 Coefficients of Elasticity of the Complex Exponential
Production Function with Real Coefficients . . . . . . . . . . . . . . . . . 207
6.6 Power Production Function of Complex Variables
with Complex Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
6.7 Logarithmic Production Function of Complex Variables . . . . . . . . 221
6.8 Exponential Production Function of Complex Variables . . . . . . . . 226
6.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
7 Multifactor Complex-Valued Models of Economy . . . . . . . . . . . . . . 233
7.1 General Provisions of Complex-Valued Model Classification . . . . 233
7.2 Linear Classification Production Function . . . . . . . . . . . . . . . . . . 237
7.3 Classification Production Function of Cobb-Douglas Type . . . . . . 242
7.4 Elasticity and Other Characteristics of a Classification
Production Complex-Valued Function . . . . . . . . . . . . . . . . . . . . . 246
7.5 Classification Power Production Function . . . . . . . . . . . . . . . . . . 256
7.6 The Shadow Economy and Its Modeling by Means
of Complex-Valued Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . 259
7.7 Formation of Complex, Multifactor Models
of Complex Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
7.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
8 Modeling Economic Conditions of the Stock Market . . . . . . . . . . . . 269
8.1 Stock Market Indexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269
8.2 Phase Plane and K-patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282
8.3 Mathematical Models of K-Patterns . . . . . . . . . . . . . . . . . . . . . . . 287
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290
9 Modeling and Forecasting of Economic Dynamics
by Complex-Valued Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
9.1 Ivan Svetunkov’s Model for Short-Term Forecasting . . . . . . . . . . 291
9.2 Complex-Valued Autoregression Models . . . . . . . . . . . . . . . . . . . 296
9.3 Solow’s Model of Economic Dynamics and Its
Complex-Valued Analog . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301
9.4 Modeling Regional Socioeconomic Development . . . . . . . . . . . . . 304
9.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318

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Complex-Valued Modeling in Economics and Finance.rar (2.28 MB, 需要: 15 个论坛币) 本附件包括：
Chapter 4.pdf
Chapter 5.pdf
Chapter 6.pdf
Chapter 7.pdf
Chapter 8.pdf
Chapter 9.pdf
Front Matter.pdf
Chapter 1.pdf
Chapter 2.pdf
Chapter 3.pdf