Operator geometric stable laws

Tomasz J. Kozubowski, Mark M. Meerschaert, Anna K. Panorska and Hans-Peter Scheffler

Journal of Multivariate Analysis, 2005, vol. 92, issue 2, 298-323

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.

Keywords: Currency; exchange; rates; Domains; of; attraction; Geometric; stable; law; Heavy; tails; Infinite; divisibility; Linnik; distribution; Operator; stable; law; Randomized; sum; Skew; Laplace; law; Stability; Stable; distribution (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (1)

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