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Operator geometric stable laws

Author

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

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.

Suggested Citation

  • Kozubowski, Tomasz J. & Meerschaert, Mark M. & Panorska, Anna K. & Scheffler, Hans-Peter, 2005. "Operator geometric stable laws," Journal of Multivariate Analysis, Elsevier, vol. 92(2), pages 298-323, February.
    • Handle: RePEc:eee:jmvana:v:92:y:2005:i:2:p:298-323
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    References listed on IDEAS

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    5. Kozubowski, Tomasz J. & Panorska, Anna K., 1998. "Weak Limits for Multivariate Random Sums," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 398-413, November.
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    8. Kozubowski, Tomasz J. & Rachev, Svetlozar T., 1994. "The theory of geometric stable distributions and its use in modeling financial data," European Journal of Operational Research, Elsevier, vol. 74(2), pages 310-324, April.
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    11. repec:nys:sunysb:93-02 is not listed on IDEAS
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    1. Kozubowski, Tomasz J. & Meerschaert, Mark M., 2009. "A bivariate infinitely divisible distribution with exponential and Mittag-Leffler marginals," Statistics & Probability Letters, Elsevier, vol. 79(14), pages 1596-1601, July.

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