Handbook of Heavy Tailed Distributions in Finance

Chapter 15

Portfolio Modeling With Heavy Tailed Random Vectors

Mark M. Meerschaert [e-mail]    Department of Mathematics, University of Nevada, Reno, USA

Hans-Peter. Scheffler [e-mail]    Fachbereich Mathematik, University of Dortmund, 44221 Dortmund, Germany

ABSTRACT

Since the work of Mandelbrot in the 1960s there has accumulated a great deal of empirical evidence for heavy tailed models in finance. In these models, the probability of a large fluctuation falls off like a power law. The generalized central limit theorem shows that these heavy-tailed fluctuations accumulate to a stable probability distribution. If the tails are not too heavy then the variance is finite and we find the familiar normal limit, a special case of stable ...