Poly%205-6.ppt - Poly Lecture 5-6 Complexity & Risk...

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Poly Lecture 5-6 Complexity & Risk Management
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Concepts,Definition Complexity Emergence Selforganization Percolation theory Chaos theory Fractals and Chaotic structures Network theory Degeneracy Evolution Agent Based Models Bottom up
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Complexity Complicated: Independence Scientists can reduce the system to its atomic elements Complexity: Interdependence Social agents need to predict the behavior of other agents agent interractions become highly nonlinear. Stability comes from the independence of noise CLT, Gaussian.
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Automata Automata network is a graph where each vertex takes states in a finite set. The state of the vertex changes in time according to a rule that only depends on the states of the neighboring vertices. State-space. Individuality (state) Cellular Automata Networks
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Emergence & Selforganization Emergence: global behavior emerges from local behavior of a system. Gestalt refers to pre-given coherent entity, static; Emergence is dynamic Branches of “emergence”: Complex adaptive systems theory, how interracting agents produce macro properties. Chaos Theory, Nonlinear dynamical systems theory: attractors are emergent phenomena. Far-from-equilibrium thermodynamics [Prigogine dissipative structures]
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Complexity Rising Scale: Under independence components are irrelevant Human organization : reinforcing contingencies.
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Complexity Profile
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Complexity Profile The complexity profile is a mathematical tool that is designed to capture important aspects of the relationship between the behavior of parts of a system and the behavior of the entire system. Behaviors of the system are assigned a scale which is related to the ability of an observer to see that behavior. Typically, larger scale behaviors involve coordination between more parts and/or larger amounts of energy. The complexity profile counts the number of behaviors that are observable at a particular scale, which includes all behaviors assigned to that scale or larger scales. When a system is formed out of independent parts, the behaviors are on a small scale. When a system is formed out of parts that all move in the same direction, the behavior is on the largest scale. When a system is formed out of parts whose behaviors are partially correlated and partially independent then as we look at the system on finer and finer scales we see more and more details. This is characteristic of complex systems formed out of specialized and correlated parts. Such systems have a complexity profile that declines gradually with scale.
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The complexity profile of a human being is a smoothly falling curve because there are various scales at which details of the internal behavior of parts of a human being become visible. For example, at the atomic scale the motion of individual atoms is visible, but most of these motions are not visible at the cellular scale. When considering the collective
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This note was uploaded on 04/05/2010 for the course FINANCE AN FRE6041 taught by Professor Taleb,nassimn during the Spring '09 term at NYU Poly.

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Poly%205-6.ppt - Poly Lecture 5-6 Complexity & Risk...

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