Honours Finance Advanced Topics in Finance: Nonlinear Analysis

1
Honours Finance (Advanced Topics in Finance
Nonlinear Analysis)

• Lecture 7 New trends in Finance Econophysics

2
Why econophysics?

• MANY reasons but
• Two stand out
• Because weve solved all the big problems in
  physics
• Remark by physicist Cheng Zhang at 1st
  Econophysics Conference, Bali 2002, in response
  to question from economist Paul Ormerod
• Because one dominant concept in modern physics is
  highly applicable to finance uncertainty
• Pre-Einsteinian physics based on uniformity
  certainty
• Newtonian Laws of Motion circa 1700s
• Supplemented by Maxwells equations for
  electromagnetic phenomena circa 1800s
• La Places conceit Give me the equations for
  the universe I can predict not just the future
  but also the past

3
A Quick Physics Primer

• By late 19th century, just two anomalies
• Speed of light
• Light seen as wave
• Waves presumed to move through medium
• E.g., sound waves are cyclic compression/expansion
  of air molecules
• Light thought to move through aether
• Unobserved substance thought to permeate all
  space
• Aether fixed, universe moves with respect to it
• IF aether exists Earth moving through it, THEN
  speed of light in one direction (forward into
  aether) should be slower than other (backwards
  with aether)
• Michelson-Morley experiment speed of light
  constant in all directions

4
A Quick Physics Primer

• Black body radiation problem
• Atom known to exist
• Model of atom was positive nucleus orbited by
  negative electrons
• By Maxwells Newton equations, orbiting charge
  should radiate energy
• Electron should rapidly spiral into nucleus
• Black bodies (i.e. any object, not just heated
  ones) should radiate energy
• Fitted to experimental data, model predicted
  EITHER infinite energy at low frequency OR
  infinite energy at high energy
• Actual energy profile was a hump
• Theory could fit one side or other but not both

5
A Quick Physics Primer

• Einstein/Planck solutions to dual problems
• light comes in small discrete packets called
  quanta
• Energy not continuous but discrete with minimum
  unit Plancks constant
• Probability uncertainty became essential
  aspects of physics
• Physics also accepted Boltzmanns Laws after
  strong 19th century resistance
• Progression of energy from highly ordered to
  disordered state increase in entropy
• All work involves generation of wasted energy
  work (desired) necessitates heat undesired but
  unavoidable)
• Combination of ideas develops measure of
  knowledge called Shannons entropy

6
A Quick Physics Primer

• Later refinements of Einstein-Planck physics
• Deterministic general theory of relativity
• Highly successful model of universe on large
  scale
• Speed of light, relativistic mass effects,
  gravity bending of light
• Probabilistic quantum theory of matter
• Bizarre experimental outcomes
• Double slit experiment
• Photons etc. interfere with each other even
  when emitted singly
• Dominant Copenhagen interpretationobserver
  affects outcomebut many others
• Essential some form of uncertain simultaneity
  between quantum-entangled particles
• Theorems/measurement derived from huge
  experimental base

7
A Quick Physics Primer

• Experiments involve massive particle
  accelerators
• Electro-magnetic cylinders pushing particles in
  near vacuum to near light speed
• Into collision with other particles
• Massive sprays of fundamental particles
  (leptons, muons, bosons, quarks) analysed by
  sensitive detectors
• Heavy-duty statistical apparatus developed to
  cope with data (computer hardware software,
  mathematical theorems)
• Many other areas of analysis opened up with
  computing (e.g., Josephson junction circuitry,
  quantum tunnelling circuitry, quantum
  computing) but no breakthroughs
• Physicists also develop complexity theory as
  explanation for large-scale phenomena (many
  standard deviations events) regularly seen in
  physical data (weather, earthquakes)

8
A Quick Physics Primer

• Todays unresolved boundaries
• Conflict between relativity quantum mechanics
  on scale of very small very new
• First microseconds of universe
• Behavior of matter at black holes, etc.
• Main theoretical development string theory
• Matter as multi-dimensional vibrating strings
• Standard models universe 10-11 dimensional
• Only 4 dimensions (space time) visible to us
• Tiny fraction of physicists now working on this
  at highly abstract level (but still with
  experimental-theoretical interplay
• Experiments needed for string theory
  controversies prohibitively expensive

9
Enter econophysics

• Some physicists (e.g., Cheng Zhang, Joe McCauley,
  Tsallis) had innate curiousity about economics
  social phenomena
• Large numbers physics graduate students with
  little possibility of experimental
  apprenticeship
• Huge body of pure financial data available for
  experimental analysis
• Clear (and, to physicists, strange but not
  unfamiliar) signs of discord in
  economic/financial theory
• Planck on acceptance of his ideas in physics An
  important scientific innovation rarely makes its
  way by gradually winning over and converting its
  opponents it rarely happens that Saul becomes
  Paul. What does happen is that its opponents
  gradually die out, and that the growing
  generation is familiarised with the ideas from
  the beginning. (M. Planck, in G. Holton (Ed.),
  Thematic Origins of Scientific Thought, Harvard
  University Press, Cambridge, MA, 1973 in
  Scientific Autobiography, New York Philosophical
  Library, New York, 1949.)

10
Enter econophysics

• A research paradigm develops
• Why not apply tools of theoretical physics to
  large body of financial data see what we find?
• Large number of regularities seen by physicists
  with respect to advanced physics that, from
  neoclassical economics point of view, were
  anomalies
• Distributions of financial data follow Power /
  Zipf / Pareto Distributions
• Standard characteristic of highly interacting
  nonlinear nonequilibrium processes
• Versus neoclassical belief data should follow
  innately random distributions since markets
  assumed to be rational, rational defined as
  all knowing, system assumed stable
• Huge baggage of a priori assumptions at conflict
  with data

11
Enter econophysics

• Main areas of research
• Statistical patterns in finance
• Also income distribution, firm sizes, extinction
  patterns
• Initially chaos (Mandlebrot etc.) but
  subsequently Power Laws, Zipf Laws, Pareto,
  Exponential, Levy Gamma distributions now
  Tsalliss q nonextensive statistical
  mechanics
• Parsimonious models of financial market
  behaviour
• El Farol model Minority Game
• Little work to date in alternative economic
  foundations
• May come with time, and will probably be
  radically different to either neoclassical or
  classical foundations

12
Statistical Patterns

• Perspective of econophysicists very different to
  neoclassical economists (and other victims of
  equilibrium thinking)
• Statistical physicists, myself included, are
  extremely interested in fluctuations. In the
  field of economics, we find ourselves surrounded
  by fluctuationswere it not for economic
  fluctuations, economists would have no work to
  do. Gene Stanley, (editor Physica A journal of
  inter-disciplinary physics) 2000, Exotic
  statistical physics Applications to biology,
  medicine, and economics, Physica A 285 1-17.
• Versus mechanisms that achieve equilibrium
  focus of standard economic paradigm

13
Statistical Patterns

• What do we do when we carry out research on
  economic fluctuations? Our approach has been to
  use our experience in critical phenomena research
  and assume that when we see fluctuations,
  correlations may be present. (10)
• A search for feedback effects between data rather
  than assumption of independence
• Main finding events that are rare by 8 orders
  of magnitudeevents that occur once in every 100
  million tradesfall on the same curve as everyday
  events. (12)
• Subsumes results with all distribution types
• Inspiration for main theoretical development
  nonextensive statistical mechanics
• Commenced with Mandlebrots work on fractals in
  1960s

14
Mandelbrot, fractals, chaos

• Mandelbrot began research in economics into
  income distribution
• Vilfredo Pareto in late 1800s noticed Power Law
  in income distribution
• Number of people N earning more than x follows
  formula
• log N log A m log x (A, m constants)
• In 1961 by chance saw graph of cotton prices that
  mirrored data on income distribution
• Noticed scale invariance as a feature of
  economic data argued fundamental feature of
  financial data
• BUT ignored in favour of The New Finance of
  Sharpe CAPM!
• Shifted into geography geometry now insights
  re-emerging as foundation of new approach to
  finance

15
Power (and other) Laws

• Power Laws, Zipf Laws, Pareto Laws all relate to
  distributions in which elements in the system
  affect each other very strongly and nonlinearly
• Resulting patterns appear random but are not
• Compared to truly random data, have many more
  extreme events
• But random processes can be generated by strongly
  chaotic processes!
• Difference appears to lie in mixing random
  processes achieve strong mixing of elements
  chaotic processes lead to patterns of
  self-similarity, not uniformity
• Area still very speculative but clearly on track
  to much more successful theory of finance than
  CAPM

16
Non-extensive statistical mechanics

• The basics Entropy
• Boltzmann-Gibbs statistical mechanics
• Shannon information theory
• Advanced non-extensive statistical mechanics
• After the hairy stuff, a quick survey of major
  trends in econophysics

17
Entropy
Warning!
Warning!

• Entropy is

Mind-bending material approaching!

• Best introduced by jokes
• The 3 laws of thermodynamics are
• 1. You can't win.
• 2. You can't even break even.
• 3. You can't get out of the game.
• A more informative version
• 1. You can't win, you can only break even.
• 2. You can only break even at absolute zero.
• 3. You can never reach absolute zero.

18
Entropy the 2nd law

• Starting at the beginning
• Key concept in science in general is conservation
  law some key entity is conserved through a
  series of transformations
• In physics, its energy
• 1st law is Law of Conservation of Energy
  Energy can change form but cannot be created or
  destroyed
• Hence You cant win
• Not a priori belief (like economics law of one
  price or other empirically false propositions)
  but expression of observed regularity
• Form of energy can change but amount of energy in
  a system remains constant
• Define overall energy as U and two
  transformations of it as Q (heat) W (work)

19
Entropy

• Then DUQW0
• Rule first developed in experiments with steam
  engines where focus was on inputting heat
  (burning coal) and getting out work (turning a
  shaft), so expressed as
• DUQ-W
• Just a convention reflecting heat in, work out
• Objective of engineers was to achieve maximum
  conversion of heat (Q) into work (W), but found
  waste heat always generated.
• Puzzle became why?
• Solved by imagining ideal device that converted
  all energy of system U into work W and then
  extending analysis to non-ideal systems (compare
  this to economics)

20
Entropy

• Basic model piston moving weight

• If weight removed from piston, then gas would
  move piston to new location where pressure in gas
  balanced weight of piston

Weightat height H
CylinderVolume V

• What if weight consisted of many fine grains of
  sand one was removed at a time?
• How far could piston itself raise the sand?
• How much work could the piston do on the sand?

PistonArea A
GasPressure P
21
Entropy

• Upwards force from compressed gas equals Pressure
  P times area of piston A
• At start of process, weight stationary gas at
  pressure P
• Forces must then be in balance
• Force of gas (P.A) just equals downwards force of
  gravity on weight
• If weight moves small dh distance then change in
  volume dV equals A times dh
• Work done is integral of force over distance it
  operates

where
so that
22
Entropy

• In ideal cylinder (all energy converted into
  work), work equals integral of pressure with
  respect to volume
• In 0 efficiency cylinder (all energy converted
  into heat), heat equals integral of temperature
  with respect to something well label S for
  now.
• In between, the rule applies that

• Change in energy equals heat plus work becomes
• Change in energy Temperature times change in
  Entropy Pressure times change in Volume
• (change in volume is workuseful expenditure of
  energy)
• So how efficient can a working engine be?

23
Entropy

• Basic cycle of internal combustion engine is
• Piston at top of cylinder pressure temperature
  low
• Call Volume V1, Pressure P1, Temperature T1
• Piston pushed by crankshaft pressure increased
• Temperature necessarily rises
• Volume V2, Pressure P2, Temperature T2
• Gas ignited
• Temperature rises dramatically
• Volume V3V2, Pressure P3P2, Temperature T3
• Piston pushed back to starting position
• Temperature falls, volume rises, pressure drops
• Volume V4V1, Pressure P4, Temperature T4
• Hot gases expelled
• Return to V1, P1, T1

24
Entropy

• Perfect efficiency engine now assumed no
  friction losses etc., all processes involve only
  changes in pressure or temperature, not both at
  once
• Change in energy of perfect gas given by heat
  capacity times change in temperature e.g. heat
  capacity 5 units
• Example temperatures of
• T1300K (Kelvin or temperature above absolute
  zero)
• T2400
• T31600
• T4600
• Can now apply

• where at each stage either dS0 or dV0 (perfect
  efficiency)

25
Entropy

• Stage 1 all compression, dS0. So

• (work in so negative work output)

• Stage 2 all temperature change, dV0. So

• Stage 3 all expansion, dS0. So

• Stage 4 all temperature change, dV0. So

• Work sum is -50050004500
• Energy input is 6000
• Ratio is efficiency of perfect engine
  4500/600075

26
Entropy

• Actual engine has lower efficiency
• Conversion of some compression into temperature,
  some rise in temperature into rise in volume
• As well as the usual suspects friction, etc.
• Typically achieve only half ideal ratio.
• Whats the problem?
• Truly ideal engine design reveals part of cause
• Carnot (1824) imagined perfect heat-exchange
  engine
• Found engine had to discharge heat to perform
  work
• Efficiency function of discharge temperature
  level
• Only if discharge temperature was absolute zero
  could engine be 100 efficient

27
Entropy Carnot engine

• During initial expansion phase, gas in cylinder
  kept at constant temperature TH heat QH must be
  added

• During work expansion phase, temperature drops
  because volume expands W extracted

• During initial contraction phase, gas in cylinder
  kept at constant temperature TC heat QC must be
  extracted

• During final contraction phase, temperature rises
  because volume contracts

28
Entropy Carnot engine

• Since engine repeats cycle, energy change over
  whole cycle zero so Work extracted must equal
  sum of heat input extraction

• Engine efficiency is ratio of work output to
  energy input

• There is a simple relationship between Q and T

• So energy efficiency can only be 100 of TC0
  Kelvin

• Also explains why high temperature engines are
  more efficient

29
Entropy

• So something in nature means that no work
  process can occur without generating waste heat.
• That something is 2nd law of thermodynamics
  entropy increases where entropy is the S in

• General statement For any process by which a
  thermodynamic system is in interaction with the
  environment, the total change of entropy of
  system and environment can almost never be
  negative. If only reversible processes occur, the
  total change of entropy is zero if irreversible
  processes occur as well, then it is positive.
• S taken as measure of disorder of system since
  related by Boltzmann Gibbs to the number of
  distinguishable states W that a system can be in
  by

30
Entropy

• Boltzmanns formula linked to structure of matter
  by concept of microstates
• Overall state (temperature, pressure, etc) of
  given system reflects ensemble of states of
  constituents (atoms, molecules, etc.)
• State of constituents reflects
• How many ways constituents can be organised
• Number of constituents having each possible state
• E.g., consider placing colour squares on 4x4 grid

• Say 1st square is red can be placed in any of 16
  locations

1

• Next e.g. blue placed in any of 15
• 16!20,920,000,000,000,000 possible combinations!

31
Entropy

• But say there is 1 red, 3 green, 5 blue, 7 orange
  squares in ensemble. Then

• are different combinations but cant be
  distinguished from each other

and

• Ditto for other arrangements of other colours
  (numbers there just to show difference)
• To compensate, have to divide 16! by product of
  all possible ways of achieving identical
  microstates
• Divide by 1! x 3! x 5! x 7!3,628,800, leaving
  5,765,760 distinct arrangements
• General formula is

32
Entropy

• Can also be put as

• Where W is number of discrete microstates system
  can be in and pi is probability of the ith such
  state
• Entropy as defined here applies to ergodic
  systems
• dynamics whose time averages coincide with
  ensemble averages (Tsallis et al. 2003,
  Nonextensive statistical mechanics and
  economics, Physica A 324 89-100)
• Colloquially, systems that converge to or orbit
  long run equilibrium values that over time fill
  the entire phase space

33
Entropy

• Consider our 4x4 grid
• Imagine these represent entities in a dynamic
  system
• E.g., gas molecules in a tiny container
• Odds of squares being in highly ordered initial
  state (all similar colours next to each other)
  very low

• Many more ways for squares to be in more
  disordered arrangement than one where all
  colours are mixed up
• Over time, each square will spend 1/16th of its
  time in each of 16 possible positions (time
  averages coincide with ensemble averages)

• But far from all (physical or social) systems
  have this characteristic

34
Entropy

• For example, Lorenzs model

• Complex dynamics means time average very
  different to average over phase space because
  system never goes near equilibria

35
Entropy

• Problem of failure of deep, established concept
  like Boltzmann-Gibbs entropy to characterise many
  real world systems troubled physicists,
  statisticians
• Ironically, CAPM analysis of derivatives
  (Black-Scholes) related to this area
• Many alternative characterisations proposed
• Power Laws
• Hurst exponents
• Best to date is revised version of
  Boltzmann-Gibbs entropy suggested by Tsallis in
  1985
• Sheer intuitionnot derived but guessed at.
• Interesting example of how scientific advance can
  occur. In his words

36
Nonextensive Statistical Mechanics

• A MexicanFrenchBrazilian workshop entitled
  First Workshop in Statistical Mechanics was
  held in Mexico City, during 213 September 1985
  That was the time of fashionable multifractals
  and related matters. During one of the coffee
  breaks, everybody went out from the lecture room,
  excepting Brezin, a Mexican student , and
  myself Brezin was explaining something to the
  student. At a certain moment, he addressed some
  point presumably related to multifractalsfrom my
  seat I could not hear their conversation, but I
  could see the equations Brezin was writing. He
  was using pq, and it suddenly came to my
  mindlike a flash and without further
  intentionthat, with powers of probabilities, one
  could generalize standard statistical mechanics,
  by generalizing the BG entropy itself and then
  following Gibbs path. Back to Rio de Janeiro, I
  wrote on a single shot the expression for the
  generalized entropy, namely

Tsallis 2004 727
37
Nonextensive Statistical Mechanics

• Why does it matter?
• q 1 returns standard distributions
• q gt 1 privileges common events
• Common (near mean events) occur more frequently
  than for Gaussian/standard entropy distributions
  and
• rare events will lead to large fluctuations,
  whereas more common events will result in more
  moderate fluctuations.
• A concrete consequence of this is that the BG
  formalism yields exponential equilibrium
  distributions (and time behavior of typical
  relaxation functions), whereas nonextensive
  statistics yields (asymptotic) power-law
  distributions (Tsallis et al. 2003 91)
• Tsalliss q may capture interactive instability
  of finance markets. Tsallis distributions fit
  finance data accurately with q1.4

38
Nonextensive Statistical Mechanics

• E.g., Stock market returns for top ten stocks on
  NYSE

Dotted line is the Gaussian distribution 2-
and 3-min curves are moved vertically for display
purposes Far better fit to data than CAPM
models

• Many other areas where Tsalliss q enables
  accurate fit to data whereas standard extensive
  statistics models (Black-Scholes, CAPM, EMH etc.)
  do not

39
Econophysics

• Tsalliss analysis may become foundation of all
  other statistical analysis by econophysicists
• In meantime, many other areas where skills
  technologies of physicists are being applied.
  E.g.
• Sornettes analysis of asset bubbles and bursts
• Minority Game parsimonious model of finance
  markets
• Scarfettas analysis of income distribution
• Ponzis model of multi-sectoral dynamics
• Many others can be found at
• http//www.unifr.ch/econophysics/

40
Why Stock Markets Crash

• Sornette geophysicist
• Study of earths dynamics
• Developed theory of earthquakes as extension of
  Per Baks theory of self-organised criticality
• Classic model the sand pile
• Pour sand onto surface one grain at a time
• For a while, pyramidal shape forms
• Slope of pyramid gets steeper
• Slope then collapses in avalanche
• One grain of sand causes more than one to fall in
  a chain reaction
• Collapse of pyramid reduces slope below critical
  level
• Pyramid reforms process repeats

41
Why Stock Markets Crash

• Sornettes earthquake model similar with tectonic
  plates as the grains of sand, motion of earths
  core as pouring force
• Movement of molten core causes plates to move on
  surface
• Increasing tension between plates causing
  vibrations that increased over time
• Release in large scale earthquake
• Decreasing tension between plates over time
  process repeats
• Pattern captured by log periodic function
• Applied to stock market where collective
  interactions between agents leading to a cascade
  of amplifications replace movement of plates

42
Why Stock Markets Crash

• Basic function for change of index is of the form

• Predicts increasing frequency of fluctuations as
  critical time approaches
• Problem is to identify critical time!

43
Why Stock Markets Crash

• On other side of crash, critical time known
• Curiosity now is does crash fit log-periodic
  form?
• Graph fits US SP500 to function

• Problems develop when extended further in time
• Tectonic plate dynamics dont change on human
  time scale finance markets economies do
• But clear relevance of log periodic form to
  short-term market movements before/after crash

44
The Minority Game

• Minority Game development begun by economist
  Brian Arthur
• Model was El Farol Irish (yes, Irish!) pub in
  Santa Fe
• Popular after-hours venue but only pleasant when
  neither empty nor full
• Problem how to predict whether worth attending a
  given night?
• Arthurs model 100 Irish music fans in Santa Fe
  bar only enjoyable when less than 40 attend a
  night
• Fans decide whether or not to attend based on
  various strategies
• A minority game you win by being in the
  minority
• Therefore no equilibrium any winning strategy
  will break down as other agents adopt it

45
The Minority Game

• Extended by Yi-Cheng Zhang others to Minority
  Game
• Artificial stock market in which winning strategy
  is to sell when majority is buying, buy when
  majority selling
• Realisation that MG isnt a complete model
• In financial trading, often it is convenient to
  join the majority trend, not to fight against the
  trend. During the Internet stock follies, it was
  possible to reap considerable profits by going
  along with the explosive boom, provided one got
  off the trend in time. There are many other
  situations where success is associated with
  conforming with the majority.
• But proposition that might still be on the
  money because

46
The Minority Game

• majority situations may actually have minority
  elements embedded in them. The real financial
  trading probably requires a mixed
  minority-majority strategy, in which timing is
  essential. The minority situations seem to
  prevail in the long run because speculators
  cannot all be winners. Indeed no boom is without
  end, being different from the crowd at the right
  time is the key to success. In a booming trend,
  it is the minority of those who get off first who
  win, the others lose. (Damien Challet, Matteo
  Marsili, Yi-cheng Zhang 2003, Minority Games,
  Oxford University Press, Oxford, 12-13)

47
A two-part income distribution model

• Basic Econophysics model a Power Law
• Implies increasing concentration all the way up
• Actual empirics of US data suggested a tail (low
  income) that didnt fit Power Law
• An empirical distribution of wealth shows an
  abrupt change between the lowmedium range, that
  may be fitted by a non-monotonic function with an
  exponential-like tail such as a gamma
  distribution, and the high wealth range, that is
  well fitted by a Pareto or inverse power-law
  function. (Nicola Scafetta, Sergio Picozzi and
  Bruce J West, 2004, An out-of-equilibrium model
  of the distributions of wealth, Quantitative
  Finance 4 353)

48
A two-part income distribution model

• Scarfetta et al suggest
• Top end (rich) due to investment
• Power Law wealth distribution generates matching
  income one
• Bottom end (poor) due to trade which is biased in
  favour of poor
• Hard to explain from neoclassical foundation
• Neoclassic economists do not expect trade to
  involve a transfer of wealth, but rather an
  increase in utility for both parties with a zero
  net transfer of wealth.

49
A two-part income distribution model

• Scarfetta et al. propose
• in trades there may be a transfer of wealth from
  one agent to the other because the price paid
  fluctuates around an equilibrium price ( value)
  and, therefore, the price may differ from the
  value of the commodity transferred
• (b) in a trade transaction the amount of wealth
  that may move from one agent to the other is
  bounded because the price and the value of a
  commodity cannot (usually) exceed the wealth of
  the poorer of the two traders
• (c) the price is socially determined in such away
  that the trade is statistically biased in favour
  of the poorer trader.

50
A two-part income distribution model

• In fact results validate my interpretation of
  Marx on value
• Marx spoke of the relationship between the wage
  and the value of labour-power, he used the term
  minimum wage, that is, a subsistence payment
  1315, thus emphasizing that in practice he
  expected the wage to exceed this minimum and
  hence there to be a price-value divergence in
  favour of the working class at the expense of
  capitalists. These effects can be incorporated
  into the social equality index f of equation (14)
  that measures the statistical bias of the trade
  in favour of the poor.

51
Multi-sectoral instability

• Physicists perception of economic cycles
• Economic dynamics is easily observed to be far
  from equilibrium where periodic recessions,
  unemployment and unstable prices occur
  persistently. An understanding of the origins of
  this behaviour from the viewpoint of complex
  dynamical systems theory would be very valuable.
  (Adam Ponzi, Ayumu Yasutomi, and Kunihiko Kaneko
  2003, Multiple Timescale Dynamics in Economic
  Production Networks, APS/123-QED
• Starting point is standard von Neumann
  equilibrium growth path

52
Multi-sectoral instability

• The VNM is defined as a static equilibrium model
  describing relationships between the variables
  which must hold at equilibrium. Equilibrium is a
  state of balanced growth where prices are
  constant. There are no dynamics defined by the
  model which might describe out of equilibrium or
  approach to equilibrium behaviour. (1)
• However it is rarely the case that economic
  processes are in equilibrium
• Their approach actual output depends on the
  quantity of the minimum of its input supplies and
  not on the quantities of its other supplies. (1)

53
Multi-sectoral instability

• Basic picture of economy reflects physics
  backgroundprocesses described as catalytic
  play important role

• A production process is the operation which
  converts one bundle of goods, including capital
  equipment, into another bundle of goods,
  including the capital equipment.

• Capital goods therefore function approximately
  like catalysts in chemical reactions, reformed at
  the end of the reaction in amounts conserved in
  the reaction. (1)

54
Multi-sectoral instability

• Model implemented as computer simulation and
  generates obvious cycles in output, prices, etc.

• Not necessarily correct model of market economy
• Constraint normally effective demand, not supply
  (stocks provide buffer)

• But useful example of dynamic multisectoral
  modelling

55
Conclusion

• Econophysics still in infancy, but
• Unencumbered by equilibrium obsession
• Equipped with advanced mathematical computing
  data analysis tools designed to cope with
  uncertainty nonlinearity
• For first time ever, a coherent group of rivals
  to neoclassicism who totally outgun it in
  technical terms
• At time of great weakness of neoclassical
  paradigm in finance
• Best chance yet for break in neoclassical hegemony