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Ubiquituous Quanta - Università
del Salento - Sept. 2013
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Can Physics contribute to a
better understanding of
problems in Economics?
Emmanuel Haven
School of Management
University of Leicester - UK

2
Structure
 Very brief overview of economic theory
milestones
 Very brief overview of financial
economics and econo-physics
milestones (i.e. statistical physics
applications)
 Brief overview of social science and
quantum physics

3
Structure (cont’d)
 Quantum mechanics and
economics/finance
 Reasonable promise…but…

4
Very brief overview of
economic theory
milestones
 Economic theory has known over the last 50
years important new developments
 In the theory of choice we can distinguish three
important models
 A first model: we have the celebrated expected
utility model of the 50’s (von Neumann and
Morgenstern 1953)
 J. von Neumann and O. Morgenstern (1953);
Theory of Games and Economic Behavior;
Princeton University Press
 The von Neumann and Morgenstern model
interpret uncertainty as objective

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economic theory
milestones (cont’d)
 The vNM model (as are others)
accept there exists a given
quantification of how likely the
various outcomes are of a decision
 This is given in the form of a
probability distribution
 See D. Kreps (1988) Notes on the
Theory of Choice, Westview Press,
Colorado- Boulder

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economic theory
 A second model: the Savage model
(1972) where uncertainty is viewed as
subjective
 L. J. Savage (1972) ; The Foundations of
Statistics, J. Wiley and Sons; New York
 There are no objective imposed
probabilities
 Probabilities are entered on the basis of
subjective preferences
 None of the uncertainty in Savage is
objective (probabilities are completely
subjective)

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economic theory
 A third model: in the Anscombe-
Aumann model (1963) we have a
mixture of objective and subjective
probabilities
 F. J. Anscombe and R.J. Aumann
(1963); A definition of subjective
probability, Annals of Mathematical
Statistics 34, 199-205

8
economic theory
 At the end of the 80’s and the 90’s further
improvements were to be noticed mainly with the work
of Machina (1989) and Gilboa et al. (1995)
 M. Machina (1989); Dynamic consistency and non-
expected utility models of choice under uncertainty,
Journal of Economic Literature 27(4), 1622-1668
 I. Gilboa and D. Schmeidler (1995); Case based
decision theory, The Quarterly Journal of Economics
110 (3), 605-639
 For instance, Gilboa et al. (1995) introduced non-
additive probabilities into the theory of risk

9
economic theory
 Outside the theory of choice we
can also mention:
 The theory of rational expectations
 T. Sargent (1986); Rational
expectations and inflation; Harper
and Row
 The theory of rational beliefs
 M. Kurz (1994b); On the structure
and diversity of rational beliefs;
Economic Theory; 4; 859-876

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Structure
We now consider:
 Very brief overview of financial
economics and econo-physics
milestones

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finance and econo-physics
milestones
 In financial economics we witness the birth of the
celebrated Black-Scholes (1973) option pricing formula
 F. Black and M. Scholes (1973); The pricing of options
and corporate liabilities, Journal of Political Economy
81, 637-659
 In 1989 we see major improvements on the CAPM
model (Breeden et al. 1989)
 D. Breeden and M. Gibbons and R. Litzenberger
(1989); Empirical test of the consumption oriented
CAPM, The Journal of Finance 44(2), 231-262

12
 The overwhelming majority of
contributions to economic theory in
the last 50 years have occurred
from economists and sometimes
mathematicians
 In the ’80 and 90’s, we can also
see contributions from physicists
and scientists of other disciplines

13
 Statistical physics made some inroads in using specific
physics concepts in especially behavioural economics
 The major protagonist in this area is Professor Eugene
Stanley – Boston University.
 Some examples of contributions (there are MANY
examples)

14
 In the area of option pricing, we note the work by
Borland (2002)
 Her work looked at accommodating option pricing with
probability density functions which are more general
than the Log-Normal density function
 Borland L. (2002); A theory of non-Gaussian option
pricing, Quantitative Finance 2(6), 415-431
 Numerous congresses have been organized
(especially: Applications of Physics in Financial
Analysis

15
Structure
We now consider:
 Brief overview of social science
and quantum physics

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Brief overview of financial
economics and quantum
physics
 I. In decision making and psychology:
 Andrei Khrennikov (2010). Ubiquitous Quantum
Structure: From Psychology to
 Finance, Springer-Verlag, Berlin, Heidelberg 2010.
 D. Aerts, J. Broekaert, L. Gabora and S. Sozzo (2013);
Quantum Structure and Human Thought, Behavioral
and Brain Sciences 36(3), 274-276.
 D. Aerts* and J. Broekaert and S. Smets (1999); The
Liar paradox in a quantum mechanical perspective,
Foundations of Science 4, 156-

17
physics
Busemeyer* et al. (2006) study a model of human
information processing from quantum mechanical
concepts
J. Busemeyer* and Wang Z. and Townsend J.T.
(2006); Quantum dynamics of human decision
making, Journal of Mathematical Psychology 50
(3), 220-241

18
physics
J. Acacio de Barros and Patrick Suppes, "Quantum
mechanics, interference, and the brain," Journal
of Mathematical Psychology 53, 306–313 (2009).
Trueblood, J. S., Brown, S. D., Heathcote, A., &
Busemeyer, J. R. (2013). Not just for consumers:
Context effects are fundamental to decision
making. Psychological Science, 24(6), 901-908.

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physics (cont’d)
 II. In game theory:
 Piotrowski et al. (2003) and Eisert* et al. (1999)
provide for an initiation to quantum games
 E. W. Piotrowski and J. Sladkowski (2003); An
invitation to quantum game theory, International
Journal of Theoretical Physics 42, 1089-
 J. Eisert* and M. Wilkens and M. Lewenstein
(1999); Quantum games and quantum strategies,
Physical Review Letters 83, 3077-3080

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physics (cont’d)
 Arfi* B. (2005); Resolving the trust
predicament: a quantum game theoretic
approach. Theory and Decision, 59 (2),
127-174

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physics (cont’d)
 III. In finance and financial economics
 Baaquie* (1995) wrote a book on
quantum finance in which option pricing
theory is explained from a path-integral
point of view

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physics (cont’d)
 B. Baaquie* (2004); Quantum Finance,
Cambridge University Press, Cambridge
 E. Haven and A. Khrennikov (2013);
Quantum Social Science, Cambridge
University Press, Cambridge
 Several articles in popular science
magazines: New Scientist

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physics (cont’d)
 Andrei Khrennikov’s paper:
 Khrennikov A. Yu. (1999); Classical and
quantum mechanics on information spaces with
applications to cognitive, psychological, social
and anomalous phenomena; Foundations of
Physics; 29; 1065-1098
 Olga Choustova’s work applies Bohmian
mechanics (a particular interpretation of
quantum mechanics) to financial economics
 O. A. Choustova, Quantum Bohmian model for
financial market, Physica A, 374, 304-314
(2006)

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physics (cont’d)
 E. Haven (2005a); Analytical solutions to the
backward Kolmogorov PDE via an adiabatic
approximation to the Schrödinger PDE, Journal
of Mathematical Analysis and Applications 311,
439-444
 E. Haven (2005b); Pilot-wave theory and
financial option pricing, International Journal of
Theoretical Physics 44 (11), 1957-1962

25
physics (cont’d)
 Segal (1998) developed work on financial option
pricing in a quantum context
 W. Segal and I.E. Segal (1998); The Black-
Scholes pricing formula in the quantum context,
Proceedings of the National Academy of
Sciences of the USA 95, 4072-4075
 Bordley* (1998) introduced a generalized
Heisenberg Uncertainty principle

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physics (cont’d)
 R. F. Bordley* (1998); Quantum mechanical and
human violations of compound probability
principles: Toward a generalized Heisenberg
uncertainty principle, Operations Research 46,
923-926
 Shubik* (1999) worked on the basics of quantum
economics
 M. Shubik* (1999); Quantum economics,
uncertainty and the optimal grid size, Economics
Letters 64 (3), 277-278

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physics (cont’d)
 Bagarello* (2006) looks at stock markets from an
operator point of view
 F. Bagarello* (2006); An operatorial approach to
stock markets, Journal of Physics A 39, 6823-
6840.

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Structure of the talk
We now consider:
 Quantum methods in economics
and finance?

29
Quantum methods in
economics and finance?
 Probabililty interference in decision
making paradoxes
 Modelling of information in finance and
economics
 This has been attempted notably with the
use of Bohmian mechanics
 How is information playing a special role
in physics?

30
Structure
We now consider:
 Reasonable promise….but….

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Reasonable
promise…but…
 What follows now – refers only to economics and
finance (and NOT to the progress made in
psychology, biology and decision making of using
physics concepts)
 There are several hurdles which need still
crossing before we can really claim physics
contributes to a better understanding of
economics
 Here are some issues – which – i think are not
easy to resolve

32
Reasonable
promise…but…
 Prob. 1: economics works with other tools
and different expectations…
 Why? A) Economic theory thrives around the use
of measure theoretical concepts. Very FEW
graduate students in economics do take courses
in PDE’s. Physicists in general are not very hot
on using measure theoretical concepts in
physics. If i) economic theory is the basis of
economics and ii) economic theory is revolving
around measure theory, then the future for
physics and economics does not bode well. B)
Also: assumptions in macroeconomics – are off
limits for many econophycists (i.e. they will not
agree with the assumptions)

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Reasonable
promise…but…
 Prob. 2: there is little integration between
economics/ financial economics and finance
 Why? The use of ‘preference modelling’ has
been done away with – squarely – in option
pricing theory
 This is the ‘bread and butter’ of economics
 Given this non-integration – it is no wonder that
physics techniques (which lean closest to option
pricing theory) do not enter into economics

34
Reasonable
promise…but…
 Prob. 3: Physical intuition of equivalent
economics based principles is sometimes
very hard to come by

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Reasonable
promise…but…
 Prob. 3: Physical intuition of equivalent
economics based principles is sometimes
very hard to come by
 The B/S Hamiltonian is a strange animal…
 Euler-Lagrange Equations (within least action)
are sometimes very difficult to interpret

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So does physics
contribute to a better
understanding of
economics?
 I want to propose two major works in the history
of economics:
 -the work by Nicolae Georgescu Roegen (a
Harvard economist): which introduced in an
implicit way entropy in economics: very few
economics students know of him!
 -the work by Louis Bachelier (and subsequently
the contribution of Paul Samuelson to this work).
Bachelier laid the groundwork of using Brownian
motion in economics (in a slightly wrong way):
very few economics students know of him!

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So does physics
contribute to a better
understanding of
economics?
 It pains me to see that in economics proper – the
concepts brought into social science by those
two luminaries – have not really penetrated...

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 THANK YOU

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