The word “quantum” is from the Latin for “how much” and in this book mathematician David Orrell shows how it applies to the world of economic transactions. Written in clear and accessible language, the book covers the essential mathematics behind topics including quantum cognition, option pricing, and quantum game theory, and delves into the nuts and bolts of quantum mechanics, the principles of quantum economic modelling, and the basics of quantum computer logic. On the way the reader will learn how quantum interference can be used to model cognitive dissonance, how a quantum walk goes further than a random walk, and how financial entanglement explains the rate of mortgage default. It is aimed at anyone who wants to understand the quantum ideas working their way into economics and finance, without getting drowned in wave equations.

As interest in quantum computing grows, many companies from established banks to startups are looking at ways to perform financial simulations using quantum algorithms. But what if we should be using quantum models anyway – because the monetary system has quantum properties of its own, and because they work?

David Orrell is an applied mathematician with extensive experience in mathematical modelling, and the author of a dozen books on science and economics.

CONTENTS

INTRODUCTION 1
Burn the mathematics 2
Quantum aversion 4
Quantum fog 6

CHAPTER 1 WHY QUANTUM? 11
Not so strange 13
A quantum of value 14
Transactions as a measurement process 15
Entanglements 17
Money creation 19
Quantum economic person 21
Dynamics 23
How much 24
Some information 26
Summary 27
Further reading 29

CHAPTER 2 SOME BASICS 30
The Hilbert space 30
Quantum measurements 33
Example: a binary decision 34
Entropic force 36
Projection sequences 37
The quarter law 39
Density matrix 40
Quantum coin 42
Summary 43
Further reading 45

CHAPTER 3 QUANTUM UTILITY 47
Expected utility theory 47
Behavioural economics 49
The sure thing effect 52
The unsure thing effect 53
Loss aversion 54
Ellsberg paradox 55
Allais effect 56
Summary 57
Further reading 58

CHAPTER 4 MENTAL INTERFERENCE 59
Wave splitter 59
The disjunction effect 61
Projection sequence 62
The attraction function 63
The conjunction effect 65
The order effect 65
Clinton and Gore 67
Summary 69

CHAPTER 5 THE QUANTUM WALK 71
Background 71
The classical random walk 72
The quantum version 73
Quantum diffusion 77
Decoherence 80
Applications 80
Summary 82

CHAPTER 6 OPTION PRICING 84
Walking the line 85
Quantum fluctuations 86
The binomial model 87
Pricing options 89
Quantum anomalies 92
Model with two assets 96
Discussion 98
Summary 99

CHAPTER 7 QUANTUM GAMES 101
Background 101
The penny flip 103
The prisoner’s dilemma 106
Entangled prisoners 107
Experiments 112
Summary 113
Further reading 114

CHAPTER 8 QUANTUM OSCILLATIONS 117
Background 118
Quantize this 119
The harmonic oscillator 122
Creation and annihilation 124
Coherent state 126
Dynamics 128
Discussion 129
Summary 130
Further reading 131

CHAPTER 9 PROBABILISTIC SUPPLY AND DEMAND 133
Background 134
Case with single buyer and seller 135
Market makers 136
Multiple agents 137
Effects on price flexibility 140
Entropic force interpretation 142
The entropic oscillator 143
Discussion 145
Summary 146

CHAPTER 10 QUANTIZED SUPPLY AND DEMAND 150
The quantum financial oscillator 151
Quantum mass 152
Quantum versus classical 154
Information exchange 157
Applications 158
Summary 160
Tables 162

CHAPTER 11 THE QUANTUM MARKET 164
Financial bosons 165
Monetary exchange 166
Cash flow 167
Quantum (in)security 169
Discussion 170
Summary 172
Further reading 173

CHAPTER 12 ENTANGLEMENTS 174
Preference reversal 175
Mortgage default 178
Quantum costs 180
Social entanglement 181
Financial entanglement 182
Entanglement versus correlation 184
Derivatives 185
Discussion 186
Summary 188
Further reading 189

CHAPTER 13 BUILDING QUANTUM MODELS 190
Principles for modelling 191
Probabilistic transactions 193
Quantum agent-based models 198
Weak foundations 200
Summary 201
Further reading 202

CHAPTER 14 CONCLUSIONS 204
The will is our pendulum 204
A new operating system 207
Shut up and calculate 208
Reasons to be quantum 210
The prediction test 212
Quantum by another name 215
Quantum calculation 217

APPENDIX QUANTUM GATES 220
Tensor product 220
Basic logic gates 221
Multiple qubits 222
Circuit representation 223
Measurement 224
Example: The quantum walk 224
Quantum programming 225

BIBLIOGRAPHY 228
INDEX 236

Errors And Typos – first printing 2020