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Keywords:

  • mathematical finance;
  • derivatives;
  • portfolio theory;
  • complexity;
  • power laws

Abstract

Outside the Platonic world of financial models, assuming the underlying distribution is a scalable “power law,” we are unable to find a consequential difference between finite and infinite variance models—a central distinction emphasized in the econophysics literature and the financial economics tradition. Although distributions with power law tail exponents α > 2 are held to be amenable to Gaussian tools, owing to their “finite variance,” we fail to understand the difference in the application with other power laws (1 < α < 2) held to belong to the Pareto-Lévy-Mandelbrot stable regime. The problem invalidates derivatives theory (dynamic hedging arguments) and portfolio construction based on mean-variance. This article discusses methods to deal with the implications of the point in a real world setting. © 2008 Wiley Periodicals, Inc. Complexity, 2009