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1. 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
2. Ubiquituous Quanta - Università
del Salento - Sept. 2013
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
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del Salento - Sept. 2013
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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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del Salento - Sept. 2013
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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
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del Salento - Sept. 2013
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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)
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del Salento - Sept. 2013
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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
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del Salento - Sept. 2013
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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
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del Salento - Sept. 2013
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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
10. Ubiquituous Quanta - Università
del Salento - Sept. 2013
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Structure
We now consider:
Very brief overview of financial
economics and econo-physics
milestones
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del Salento - Sept. 2013
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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
12. Ubiquituous Quanta - Università
del Salento - Sept. 2013
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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
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del Salento - Sept. 2013
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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)
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del Salento - Sept. 2013
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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
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del Salento - Sept. 2013
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Structure
We now consider:
Brief overview of social science
and quantum physics
16. Ubiquituous Quanta - Università
del Salento - Sept. 2013
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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. Ubiquituous Quanta - Università
del Salento - Sept. 2013
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Brief overview of financial
economics and quantum
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. Ubiquituous Quanta - Università
del Salento - Sept. 2013
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Brief overview of financial
economics and quantum
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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del Salento - Sept. 2013
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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
20. Ubiquituous Quanta - Università
del Salento - Sept. 2013
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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
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del Salento - Sept. 2013
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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
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del Salento - Sept. 2013
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Brief overview of financial
economics and quantum
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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del Salento - Sept. 2013
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Brief overview of financial
economics and quantum
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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del Salento - Sept. 2013
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Brief overview of financial
economics and quantum
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. Ubiquituous Quanta - Università
del Salento - Sept. 2013
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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
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del Salento - Sept. 2013
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Brief overview of financial
economics and quantum
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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del Salento - Sept. 2013
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Brief overview of financial
economics and quantum
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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del Salento - Sept. 2013
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Structure of the talk
We now consider:
Quantum methods in economics
and finance?
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del Salento - Sept. 2013
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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?
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del Salento - Sept. 2013
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Structure
We now consider:
Reasonable promise….but….
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del Salento - Sept. 2013
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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
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del Salento - Sept. 2013
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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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del Salento - Sept. 2013
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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
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del Salento - Sept. 2013
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Reasonable
promise…but…
Prob. 3: Physical intuition of equivalent
economics based principles is sometimes
very hard to come by
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del Salento - Sept. 2013
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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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del Salento - Sept. 2013
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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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del Salento - Sept. 2013
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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...