Transcript Nonlinear Dynamics and Complex Systems

Complexity and
Complex 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
A Personal Anecdote
• Some common student questions
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“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 won’t get bored with being an
actuary,” which morphed into
– “Where is the beauty in actuarial science?”
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
“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
Final Conclusion (1)
Complexity
Theory
Is …
Final Conclusion (1)
Total CRAP !
(discuss amongst yourselves)
Final Conclusion (2)
Complexity
Theory
Is …
Final Conclusion (2)
The Answer to All of
Life’s Problems !
(let’s go home)
Actuarial Usefulness of Such
“Popular” 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
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
Historical Background
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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.
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
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
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
xt+1 = a xt (1-xt)
– Stability depends upon the coefficient value
– Note: no noise or chaotic provision built into rule
Sante Fe Institute
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Founded in 1984
Private, non-profit
Multidisciplinary research and education
Primarily a “visiting” institution
Current research focus areas
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Cognitive neuroscience
Computation in physical and biological systems
Economic and social interactions
Evolutionary dynamics
Network dynamics
Robustness
Definitions and Properties
• Complexity
– Non-linear interaction among multiple components
– Complicated versus complex systems
•Deterministic
•Reductionist principle
•Dynamic / stochastic
•Holistic
– Irreducible
– Local and distributed
– Non-deterministic / unpredictable
– Emergence / self-organization
Definitions and Properties (cont.)
• Complex adaptive systems
– Essentially, like living biological systems
– Can learn /evolve over time
– A large number of agents which are
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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
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
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.”
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.”
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
“Wealth”
Two Contexts
(1) As an end in itself
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Aristotle, Ethics: “The end of… economics (is) wealth.
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Adam Smith: wealth an end – but also a means (e.g.,
wealth ~ power); economy is part of politics
(2) As a means or factor
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With respect to political / social power
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Relationship of wealth to virtue / sin
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Social attitudes regarding wealth (or poverty)
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
Nonlinear Modeling Techniques
• Neural networks
• Genetic algorithms
• Fuzzy logic
See Shapiro (2000), IME
• 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
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
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 Hitchhiker’s Guide to the Techniques of
Adaptive Nonlinear Models,” Insurance: Mathematics &
Economics, 26: 119-132