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Quantum Modelling of Economic and Financial Systems Selected Topics.pdf
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Selected Topics
Part I Introduction and Background
1 Underpinnings of Interdisciplinary Inquiry 3
1.1 Physics: From a Brief History to the Economic Sciences 5
1.2 Generic Structure of the Physical Theories of Motion 13
1.3 About Economics and Finance 18
1.4 About the Book 25
References 29
2 Elements of Classical and Quantum Mechanics 31
2.1 The Euler–Lagrange and the Hamilton–Jacobi Equations 32
2.2 The Idea of an Ensemble in the Classical Context 35
2.3 Continuity Equation for Particle Density 36
2.4 Classical–Quantum ‘Mash-up’ 37
2.5 The Idea of an Ensemble in the Quantum Context 40
2.6 The “Free Particle” Wave Function, Operators 41
2.7 The Uncertainty Principle, Expectation Value 42
2.8 Wave Packets 43
References 46
3 Elements of Economics 47
3.1 The Many Flavours of Economics: A Brief Introduction 47
3.2 The Twentieth Century: Economics Develops at Breakneck
Speed 49
3.3 The Observable in Twentieth-Century Economics 50
3.4 Economics and Theory Falsifcation 50
3.5 Constants and Unobservables 51
3.6 Behavioural and Experimental Economics 51
3.7 Computational Economics 53
3.8 Economics and Neuroscience: Neuro-economics 54
3.9 The Value of Information 55
References 56
4 Some Selected Financial Models 58
4.1 Introduction 58
4.2 The Kyle Model 60
4.3 The Glosten and Milgrom Model 62
4.4 Asset Prices: Trading and Trajectories 63
4.5 Toward Pricing 67
4.6 The Rosenow Model 68
References 72
Part II Quantum-like Modelling
5 Quantum-like Modelling in Economics 77
5.1 Introduction 77
5.2 Incompatibility to the Rescue in the Conjunction Fallacy 79
5.3 Earlier Ideas on the Quantum Formalism in Decision
Theory 80
5.4 Alternatives to Expected Utility 83
5.5 The QQ Equality and Nonatomic Instruments 88
5.6 The Quantum-like Version of the Aumann Theorem 90
References 91
6 Bohmian Mechanics and Finance 94
6.1 Probability Embedded (or Not) in the Social Science
Model 94
6.2 Bohmian Mechanics and Finance: The Groundwork 96
6.3 Bohmian Mechanics and Finance: Financial Information 100
6.4 Quantum Pilot-Wave Theory and a Macroscopic Fluid
System 101
References 103
ix Contents
7 Other Quantum-like Models in Finance 105
7.1 Quantum Harmonic Oscillators and Quantum Probability 105
7.2 Quantum Option Pricing with the Aid of Quantum
Probability 107
7.3 Quantum Probability Applied to Investment Choice 108
7.4 Quantum Probability and Process Mining 109
7.5 Quantum Counting and Open Systems in Social Science 110
7.6 Non-Hermitian Hamiltonians in Finance 112
7.7 Quo Vadis: Expanding Mathematical Modelling? 112
7.8 Quo Vadis: Limitations of Mathematical Modelling? 117
References 118
Part III Quantum Physics-like Modelling
8 Motivations and Foundations 123
8.1 On the ‘Physical’ Foundations of Quantum Theory 126
8.2 Agent-Centric Quantum Physics-like Models:
Expectations 135
8.3 Analogies and Analogical Arguments: Selected Topics 139
8.4 Analogies and Analogical Arguments: Key Takeaways 148
References 154
9 Single-Particle Systems versus Agents – I 156
9.1 Quantum Behaviour of Electrons: Two-Slit Interference 158
9.2 From Electrons to Agents: The Analogy Checklist 161
9.3 Quantum Behaviour of Agents: Two-Preference
Interference 165
References 169
10 Single-Particle Systems versus Agents – II 170
10.1 Electrons versus Agents: V = 0 173
10.2 Electrons versus Agents: V = −Kx 177
10.3 A Word on the Model Assumptions 178
References 180
11 Simulations and Interpretations 181
11.1 Simulations of Probability Distributions and Trajectories 181
11.2 Interpretations of the Model Parameters 191
References 196
x Contents
12 Future Directions 197
12.1 Potential Energy and Agent Heterogeneities 198
12.2 Connections with the Previous Finance Models 200
12.3 Tenets: From Physics to the Economic Sciences 201
12.4 Electrons versus Agents: The Issue of ‘Free Will’ 203
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