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Ubiquituous Quanta - Università del Salento - Sept. 2013 1

Can Physics contribute to a better understanding of problems in Economics?

Emmanuel Haven School of Management University of Leicester - UK


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


Structure (cont’d) Quantum mechanics and

economics/finance Reasonable promise…but…


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


Very brief overview of 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


Very brief overview of economic theory milestones (cont’d) 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)


Very brief overview of economic theory milestones (cont’d) 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


Very brief overview of economic theory milestones (cont’d)

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


Very brief overview of economic theory milestones (cont’d) 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


Structure

We now consider: Very brief overview of financial

economics and econo-physics milestones


Very brief overview of 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


Very brief overview of finance and econo-physics milestones (cont’d) 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


Very brief overview of finance and econo-physics milestones (cont’d)

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)


Very brief overview of finance and econo-physics milestones (cont’d)

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


Structure We now consider: Brief overview of social science

and quantum physics


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-



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



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.


Brief overview of financial economics and quantum 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


Brief overview of financial economics and quantum physics (cont’d) Arfi* B. (2005); Resolving the trust

predicament: a quantum game theoretic approach. Theory and Decision, 59 (2), 127-174


Brief overview of financial economics and quantum 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



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



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)



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


Brief overview of financial economics and quantum 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



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



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.


Structure of the talk We now consider: Quantum methods in economics

and finance?


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?


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


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


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)



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



Prob. 3: Physical intuition of equivalent economics based principles is sometimes very hard to come by



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


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!


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...


THANK YOU

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