Introduction to Econophysics: Contemporary Approaches with Python Simulations
- Length: 293 pages
- Edition: 1
- Language: English
- Publisher: CRC Press
- Publication Date: 2021-10-29
- ISBN-10: 0367648458
- ISBN-13: 9780367648459
- Sales Rank: #2804952 (See Top 100 Books)
Econophysics explores the parallels between physics and economics and is an exciting topic that is attracting increasing attention. However there is a lack of literature that explains the topic from a broad perspective. This book introduces advanced undergraduates and graduate students in physics and engineering to the topic from this outlook, and is accompanied by rigorous mathematics which ensures that this will also be a good guide for established researchers in the field as well as researchers from other fields, such as mathematics and statistics, who are interested in the topic.
Key features:
- Presents a multidisciplinary approach that will be of interest to students and researchers from physics, engineering, mathematics, statistics, and other physical sciences
- Accompanied by Python code with further learning opportunities, available for readers to download from the CRC Press website.
- Accessible to both students and researchers
Carlo R. da Cunha is an associate professor of physics and engineering physics at the Universidade Federal do Rio Grande do Sul (Brazil) and has been since 2011. Dr. da Cunha received his M.Sc. Degree from the West Virginia University in 2001 and his Ph.D. degree from Arizona State University in 2005. He was a postdoctoral researcher at McGill University in Canada in 2006 and an assistant professor of engineering at the University Federal de Santa Catarina between 2007 and 2011. He has been a guest professor at the Technische Universität Wien (Austria), Chiba University (Japan) and Arizona State University (US). His research revolves around the physics of complex systems where he has been drawing parallels between physical and economic systems from quantum to social levels.
Cover Half Title Title Page Copyright Page Dedication Contents Preface Chapter 1: Review of Economics 1.1. Supply and Demand 1.2. Efficient Market hypothesis 1.3. Stocks and derivatives 1.3.1. Options 1.3.1.1. Strategies with Options Chapter 2: Asset Return Statistics 2.1. Return Rates 2.2. Probability theory 2.2.1. Probability Measure 2.2.1.1. Conditional Probability 2.2.2. σ-Algebra 2.2.3. Random Variables 2.2.3.1. Conditional Expectation 2.2.4. Distribution Functions 2.2.4.1. Moments of a Distribution 2.2.5. Lévy Processes 2.2.5.1. Infinitely Divisible Processes 2.2.5.2. Stable Distributions 2.2.6. Distribution Tails 2.2.6.1. Subexponential Distributions 2.2.6.2. Long and Fat Tails 2.2.7. Pareto Distribution 2.2.7.1. Lorenz Curve 2.2.7.2. Gini Index 2.3. Models for financial time series 2.3.1. Autoregressive Model (AR) 2.3.2. Moving Average (MA) 2.3.3. Autoregressive Moving Average (ARMA) 2.3.4. Box-Jenkins Approach 2.3.4.1. Partial Autocorrelation 2.3.4.2. Durbin-Levinson Recursive Method 2.3.4.3. Yule-Walker Equations 2.3.5. Heteroscedasticity 2.3.5.1. Generalized ARCH Model 2.4. Stylized empirical facts of financial time series 2.4.1. Stationarity 2.4.1.1. Fourier Transform 2.4.2. Common empirical facts Chapter 3: Stochastic Calculus 3.1. Martingales and fair Games 3.1.1. Random Walks 3.1.2. Pólya Processes 3.1.3. Stopping Times 3.1.4. Wald’s Equation 3.1.5. Galton-Watson Process 3.1.5.1. Extinction 3.1.6. Azuma-Hoeffding Theorem 3.2. Markov chains 3.2.1. Transition Function 3.2.2. Stationary Distribution 3.2.2.1. Detailed Balance 3.2.3. First Passage Time 3.2.4. Birth-and-Death Process 3.2.4.1. Pure Birth Process 3.2.4.2. Yule-Furry Process 3.2.4.3. Pure Death Process 3.2.4.4. Linear Birth and Death Process 3.3. Ornstein-Uhlenbeck processes 3.3.1. Langevin Equation 3.3.1.1. Solution 3.3.1.2. Dissipation-Fluctuation Theorem 3.3.2. Limited OU Process 3.4. Point Processes 3.4.1. Hawkes Process 3.4.1.1. Solution Chapter 4: Options Pricing 4.1. From a Random walk to a Wiener process 4.2. Binomial trees 4.2.1. Cox-Ross-Rubinstein Model 4.3. Black-Scholes-Merton Model 4.3.1. Diffusion-Advection 4.3.2. Solution Chapter 5: Portfolio Theory 5.1. Markowitz model 5.1.1. Risk Estimation 5.1.2. Risk-free Asset 5.1.2.1. Market Portfolio 5.1.3. Tobin’s Separation Theorem 5.1.3.1. CAPM 5.2. Random Matrix Theory 5.2.1. Density of Eigenvalues 5.2.2. Wigner’s Semi-Circle Law 5.2.3. Marčenko-Pastur Law 5.2.3.1. Correlation Matrix 5.2.4. Wigner’s Surmise 5.3. Other portfolio measures Chapter 6: Criticality 6.1. Crises and cycles 6.2. Catastrophe Theory 6.2.1. Cusp Catastrophe 6.2.2. Catastrophic Dynamics 6.3. Self-organized criticality 6.3.1. Cellular Automata 6.3.2. Simulations Chapter 7: Games and Competitions 7.1. Game theory through examples 7.1.1. the El Farol Bar Problem 7.1.1.1. Minority Game 7.1.2. Cooperative Games 7.1.3. Ultimatum Game 7.1.3.1. Nash Equilibrium 7.1.4. Prisoner’s Dilemma 7.1.4.1. Pareto Optimum 7.1.4.2. Walrasian Equilibrium 7.1.5. (Anti-)Coordination Games 7.1.5.1. Ratchet Effect 7.2. Evolutionary game theory 7.2.1. Mixed Strategy 7.2.2. Replicator Dynamics 7.3. Lotka-Volterra equations Chapter 8: Agent-Based Simulations 8.1. Complex networks 8.1.1. Metrics 8.1.1.1. Clustering Coefficient 8.1.1.2. Centrality 8.1.1.3. Assortativity 8.1.2. Random Networks 8.1.2.1. Average Path Length 8.1.2.2. Clustering Coefficient 8.1.3. Scale-Free Networks 8.1.3.1. Degree Distribution 8.1.3.2. Clustering Coefficient 8.1.4. Small World Networks 8.2. Socioeconomic models 8.2.1. Schelling’s Model of Segregation 8.2.2. Opinion Dynamics 8.2.2.1. Kirman Model 8.2.3. Market Spin Models 8.3. Kinetic Models for wealth distribution 8.3.1. Conservative Market Model 8.3.2. Non-Conservative Market Model Appendix A: Simulation of Stochastic Processes Appendix B: Monte Carlo Simulations Appendix C: Fokker-Planck Equation Appendix D: Girsanov Theorem Appendix E: Feynman-Kack Formula Appendix F: Boltzmann Equation Appendix G: Liouville-BBGKY G.1. Liouville theorem G.2. BBGKY hierarchy References Index
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