Operator geometric stable laws

Authors:
Tomasz J. Kozubowski;Mark M. Meerschaert;Anna K. Panorska;Hans-Peter Scheffler
Affiliations:
University of Nevada, Mathematics and Statistics, 084, Reno, NV;University of Nevada, Mathematics and Statistics, 084, Reno, NV;University of Nevada, Mathematics and Statistics, 084, Reno, NV;Fachbereich Mathematik, University of Dortmund, 44221 Dortmund, Germany
Venue:
Journal of Multivariate Analysis
Year:
2005

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Abstract

Operator geometric stable laws are the weak limits of operator normed and centered geometric random sums of independent, identically distributed random vectors. They generalize operator stable laws and geometric stable laws. In this work we characterize operator geometric stable distributions, their divisibility and domains of attraction, and present their application to finance. Operator geometric stable laws are useful for modeling financial portfolios where the cumulative price change vectors are sums of a random number of small random shocks with heavy tails, and each component has a different tail index.