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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

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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 won’t 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 Life’s Problems ! (let’s go home)

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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

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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 ( BC ) Pythagoras ( BC ) Euclid (c. 300 BC ) Ptolemy (c. 140 AD ) Copernicus ( AD ) Kepler ( AD ) Nineteenth-century Twentieth-century Eternal forms Primacy of numbers Cosmological system Systematic 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 x t+1 = x t (1-x t ) –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 (2)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): Craighead, 1994, “Chaotic Analysis on U.S. Treasury Interest Rates,” 4 th AFIR International Colloquium, pp 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:

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