Complexity and Complex Adaptive Systems

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Complexity andComplex Adaptive Systems

• Rick Gorvett, FCAS, MAAA, ARM, FRM, Ph.D.
• (Incoming) Director, Actuarial Science Program
• University of Illinois at Urbana-Champaign
• Actuarial Research Conference
• Iowa City, IA
• August 2004

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A Personal Anecdote

• Some common student questions
• Will this be on the exam?
• Is the final cumulative?
• What do I say at an interview?
• How do I decide between casualty and life?
• One particular (very good) student asked recently
• How do I know I wont get bored with being an
  actuary, which morphed into
• Where is the beauty in actuarial science?

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The Beauty in Actuarial Science

• Virtually everything can be considered to be
  relevant to actuarial science
• Economic and financial conditions
• Social, political, and religious conditions and
  trends
• Science, technology, medicine
• In a fast-changing, dynamic world, the profession
  must also evolve and adapt to the underlying
  factors

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Complexity Theory

• Highly visible
• Noted scholars are involved
• Santa Fe Institute
• Books for the general public
• As with anything, one needs to go into a study of
  complexity theory with an open mind
• An almost cultish following

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Final Conclusion (1)

• Complexity
• Theory
• Is

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Final Conclusion (1)

• Total CRAP !
• (discuss amongst yourselves)

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Final Conclusion (2)

• Complexity
• Theory
• Is

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Final Conclusion (2)

• The Answer to All of Lifes Problems !
• (lets go home)

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Actuarial Usefulness of SuchPopular Concepts?

• Historical lesson
• VaR (Value-at-Risk)
• 1990s concept
• But actuaries have been doing this for decades!
• Enterprise risk management (ERM)
• Also Dynamic Financial Analysis (DFA)
• Similarities to the complexity approach
• Interconnectedness

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Conceptually

• we need to overcome the idea, so prevalent in
  both academic and bureaucratic circles, that the
  only work worth taking seriously is highly
  detailed research in a specialty. We need to
  celebrate the equally vital contribution of those
  who dare to take what I call a crude look at the
  whole.
• - Murray Gell-Mann, The Quark and the Jaguar

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Historical Background

• Plato (427-347 BC)
• Pythagoras (570-490 BC)
• Euclid (c. 300 BC)
• Ptolemy (c. 140 AD)
• Copernicus (1473-1543 AD)
• Kepler (1571-1630 AD)
• Nineteenth-century
• Twentieth-century

Eternal forms
Primacy of numbers
Systematic
Cosmological system
Heliocentric circular
Ellipses
Non-Euclidean geometry
Relativity Quantum M.
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So.

• We naturally (and/or have been conditioned to)
  love and accept
• Linearity
• Smoothness
• Stability
• This, in the face of a world that is largely
• Nonlinear
• Unsmooth
• Random

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Chaos

• Random results from simple equations
• OR
• Finding order in random results
• Sensitivity to initial conditions
• Butterfly effect
• Measurement issues (parameter uncertainty)
• Local randomness vs. global stability
• Deterministic not total disorder

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Chaos (cont.)

• Consider a non-linear time series
• E.g., it can converge, enter into periodic
  motion, or enter into chaotic motion
• Example the logistic function
• xt1 a xt (1-xt)
• Stability depends upon the coefficient value
• Note no noise or chaotic provision built into
  rule

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Sante Fe Institute

• Founded in 1984
• Private, non-profit
• Multidisciplinary research and education
• Primarily a visiting institution
• Current research focus areas
• Cognitive neuroscience
• Computation in physical and biological systems
• Economic and social interactions
• Evolutionary dynamics
• Network dynamics
• Robustness

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Definitions and Properties

• Complexity
• Non-linear interaction among multiple components
• Complicated versus complex systems
• Irreducible
• Local and distributed
• Non-deterministic / unpredictable
• Emergence / self-organization

• Deterministic
• Reductionist principle

• Dynamic / stochastic
• Holistic

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Definitions and Properties (cont.)

• Complex adaptive systems
• Essentially, like living biological systems
• Can learn /evolve over time
• A large number of agents which are
• Heterogeneous
• Interact non-linearly
• Locally determined
• Open and subject to outside influences
• Not necessarily in equilibrium
• View of overall system is incomplete and
  inconsistent across agents

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With Apologies to Joyce Kilmer

• Euclidean geometry cannot replicate a tree.
  Euclidean geometry recreates the perceived
  symmetry of the tree, but not the variety that
  actually builds its structure. Underlying this
  perceived symmetry is a controlled randomness,
  and increasing complexity at finer levels of
  resolution.
• - Peters, 1994, Fractal Market Analysis
• Applying Chaos Theory to Investment
• and Economics

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Quotation

• War and Peace, by Leo Tolstoy
• Book Eleven, Chapter 1
• Only by taking infinitesimally small units for
  observation (the differential of history, that
  is, the individual tendencies of men) and
  attaining to the art of integrating them (that
  is, finding the sum of these infinitesimals) can
  we hope to arrive at the laws of history.

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Quotation (cont.)

• War and Peace, by Leo Tolstoy
• Second Epilogue, Chapter 11
• And if history has for its object the study of
  the movement of the nations and of humanity and
  not the narration of episodes in the lives of
  individuals, it too, , should seek the laws
  common to all the inseparably interconnected
  infinitesimal elements of free will.

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Social Science and Complexity

• How can it be that sciences founded on the
  mathematical linear determinism of classical
  physics have moved more quickly to the use of
  nonlinear computer models than economics and
  sociology where those doing the science are no
  different from social actors who are Brownian
  motion?
• - Henrickson and McKelvey, Foundations of
  new social science
• Institutional legitimacy from philosophy,
  complexity science,
• postmodernism, and agent-based modeling,
  Proceedings of the
• National Academy of Sciences, May 14, 2002

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Wealth

• Two Contexts
• (1) As an end in itself
• Aristotle, Ethics The end of economics (is)
  wealth.
• Adam Smith wealth an end but also a means
  (e.g., wealth power) economy is part of
  politics
• As a means or factor
• With respect to political / social power
• Relationship of wealth to virtue / sin
• Social attitudes regarding wealth (or poverty)

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Finance and Economics

• Traditional (classical) paradigm
• Random walk
• Efficient markets hypothesis
• Rational behavior
• Emerging paradigm
• Behavioral and utility issues
• Possible path-dependence
• Learning from experience

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Nonlinear Modeling Techniques

• Neural networks
• Genetic algorithms
• Fuzzy logic
• Other techniques
• Agent-based modeling
• Simple agents simple rules ? societies
• Cellular automata
• Start with simple set of rules
• Can produce complex and interesting patterns
• Percolation theory
• Lattice
• Probability associated with yes or no in each
  cell of the lattice
• Clustering and pathways

See Shapiro (2000), IME
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Final Quotation

• If Darwin had had a computer on his desk, he
  (Santa Fe Institute economist W. Brian Arthur)
  exclaims, who knows what he would have
  discovered! What indeed Charles Darwin might
  have discovered a great deal about computers and
  very little about nature.
• - John Horgan, From Complexity to Perplexity,
• Scientific American, June 1995

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Sample References

• Casti, 2003, Money is Funny, or Why Finance is
  Too Complex for Physics, Complexity, 8(2) 14-18
• Craighead, 1994, Chaotic Analysis on U.S.
  Treasury Interest Rates, 4th AFIR International
  Colloquium, pp. 497-536
• Hogan, et al, eds., 2003, Nonlinear Dynamics and
  Chaos Where do we go from here?, Institute of
  Physics Publishing
• Horgan, 1995, From Complexity to Perplexity,
  Scientific American, 272(6) p. 104
• Peters, 1994, Fractal Market Analysis Applying
  Chaos Theory to Investment and Economics, John
  Wiley Sons
• Shapiro, 2000, A Hitchhikers Guide to the
  Techniques of Adaptive Nonlinear Models,
  Insurance Mathematics Economics, 26 119-132