Statistical physics and economics: concepts, tools and applications
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY [u.a.]
Springer
2003
|
| Series: | Springer tracts in modern physics
184 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 244 S. graph. Darst. |
| ISBN: | 0387002820 |
Staff View
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Record in the Search Index
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| adam_text | Contents
1. Economy and Complex Systems 1
1.1 What Is a Complex System? 1
1.2 Determinism Versus Chaos 4
1.3 The Probability Distribution 7
1.4 The Liouville Equation 9
1.5 Econophysics 10
2. Evolution and Probabilistic Concepts 13
2.1 Some Notations of Probability Theory 13
2.1.1 Probability Distribution of Relevant Quantities 13
2.1.2 Measures of Central Tendency 14
2.1.3 Measure of Fluctuations Around the Central Tendency 15
2.1.4 Moments and Characteristic Functions 16
2.1.5 Cumulants 17
2.2 Generalized Rate Equations 18
2.2.1 The Formal Solution of the Liouville Equation 18
2.2.2 The Nakajima Zwanzig Equation 19
2.3 Combined Probabilities 24
2.3.1 Conditional Probability 24
2.3.2 Joint Probability 24
2.4 Markov Approximation 26
2.5 Generalized Fokker Planck Equation 28
2.5.1 Differential Chapman Kolmogorov Equation 28
2.5.2 Deterministic Processes 33
2.5.3 Fokker Planck Equation 34
2.5.4 The Master Equation 34
2.6 Correlation and Stationarity 35
2.6.1 Stationarity 35
2.6.2 Correlation 36
2.6.3 Spectra 37
2.7 Stochastic Equations of Motion 38
2.7.1 The Mori Zwanzig Equation 38
2.7.2 Separation of Timescales 42
2.7.3 Wiener Process 43
X Contents
2.7.4 Stochastic Differential Equations 44
2.7.5 Ito s Formula and the Fokker Planck Equation 46
3. Financial Markets 49
3.1 Introduction 49
3.1.1 Finance and Financial Mathematics Versus Econo
physics 49
3.1.2 Scales in Financial Data 51
3.1.3 Measurement of Price Fluctuations 53
3.2 Empirical Analysis 55
3.2.1 Probability Distributions 55
3.2.2 Ergodicity in Financial Data 56
3.2.3 Stationarity of Financial Markets 57
3.2.4 Markov Approximation 60
3.2.5 Taxonomy of Stocks 61
3.3 Long Time Regime 67
3.3.1 The Central Limit Theorem 67
3.3.2 Convergence Problems 72
3.3.3 Fokker Planck Equation for Financial Processes 74
3.3.4 The Log Normal Law 79
3.4 Standard Problems of Finance 80
3.4.1 The Escape Problem 80
3.4.2 The Portfolio Problem 82
3.4.3 Option Pricing Theory 86
3.5 Short Time Regime 95
3.5.1 High Frequency Observations 95
3.5.2 Levy Distributions 97
3.5.3 Convergence to Stable Levy Distributions 100
3.5.4 Scaling Behavior 101
3.5.5 Truncated Levy Distributions 106
3.6 Large Fluctuations 108
3.6.1 Extreme Value Theory 108
3.6.2 Partition Function Formalism 115
3.6.3 The Cramer Theorem 120
3.6.4 Extreme Fluctuations 122
3.6.5 A Mechanism for Extreme Price Changes 124
3.7 Memory Effects 126
3.7.1 Time Correlation in Financial Data 126
3.7.2 Ultrashort Timescales 130
3.7.3 Autoregressive Processes 143
3.7.4 Time Reversible Symmetry 152
Contents XI
4. Economic Systems 157
4.1 The Task of Economics 157
4.2 Microeconomics 165
4.2.1 The Polypolist and Stability Analysis 165
4.2.2 The Monopolist and Chaotic Behavior 170
4.3 Thermodynamics and Economy 174
4.3.1 Thermodynamic Concepts 174
4.3.2 Consumer Behavior 176
4.3.3 Thermodynamics and Environmental Economics 180
4.4 Macroeconomics 181
4.4.1 Models and Measurements 181
4.4.2 Scaling Laws and Scale Invariance 184
4.4.3 Economic Field Theories 188
5. Computer Simulations 195
5.1 Models and Simulations 195
5.2 Monte Carlo Simulations 197
5.2.1 Monte Carlo and Random Generators 197
5.2.2 Dynamic Monte Carlo 199
5.2.3 Quasi Monte Carlo 200
5.2.4 Reverse Monte Carlo 203
5.3 Cellular Automata 204
6. Forecasting 207
6.1 Regression and Autoregression 207
6.2 The Bayesian Concept 210
6.2.1 Public Surveys and Decision Making 210
6.2.2 Bayesian Theory and Forecasting 212
6.3 Neural Networks 213
6.3.1 Introduction 213
6.3.2 Spin Glasses and Neural Networks 214
6.3.3 Topology of Neural Networks 218
6.3.4 Training of Neural Networks 221
6.3.5 Neural Networks for Forecasting 223
References 227
Index 241
|
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| indexdate | 2024-07-09T19:12:21Z |
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| spelling | Schulz, Michael Verfasser aut Statistical physics and economics concepts, tools and applications Michael Schulz New York, NY [u.a.] Springer 2003 XI, 244 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer tracts in modern physics 184 Wirtschaft Economics Statistical methods Statistical physics Wirtschaftstheorie (DE-588)4079351-5 gnd rswk-swf Statistische Physik (DE-588)4057000-9 gnd rswk-swf Statistische Physik (DE-588)4057000-9 s Wirtschaftstheorie (DE-588)4079351-5 s DE-604 Springer tracts in modern physics 184 (DE-604)BV000000153 184 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010250151&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schulz, Michael Statistical physics and economics concepts, tools and applications Springer tracts in modern physics Wirtschaft Economics Statistical methods Statistical physics Wirtschaftstheorie (DE-588)4079351-5 gnd Statistische Physik (DE-588)4057000-9 gnd |
| subject_GND | (DE-588)4079351-5 (DE-588)4057000-9 |
| title | Statistical physics and economics concepts, tools and applications |
| title_auth | Statistical physics and economics concepts, tools and applications |
| title_exact_search | Statistical physics and economics concepts, tools and applications |
| title_full | Statistical physics and economics concepts, tools and applications Michael Schulz |
| title_fullStr | Statistical physics and economics concepts, tools and applications Michael Schulz |
| title_full_unstemmed | Statistical physics and economics concepts, tools and applications Michael Schulz |
| title_short | Statistical physics and economics |
| title_sort | statistical physics and economics concepts tools and applications |
| title_sub | concepts, tools and applications |
| topic | Wirtschaft Economics Statistical methods Statistical physics Wirtschaftstheorie (DE-588)4079351-5 gnd Statistische Physik (DE-588)4057000-9 gnd |
| topic_facet | Wirtschaft Economics Statistical methods Statistical physics Wirtschaftstheorie Statistische Physik |
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