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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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    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
    2. Rachev S. T. & SenGupta A., 1992. "Geometric Stable Distributions And Laplace-Weibull Mixtures," Statistics & Risk Modeling, De Gruyter, vol. 10(3), pages 251-272, March.
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    4. Kozubowski Tomasz J., 1994. "The Inner Characterization Of Geometric Stable Laws," Statistics & Risk Modeling, De Gruyter, vol. 12(3), pages 307-322, March.
    5. Mark M. Meerschaert & Hans‐Peter Scheffler, 2001. "Sample Cross‐correlations for Moving Averages with Regularly Varying Tails," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(4), pages 481-492, July.
    6. Resnick, Sidney & Greenwood, Priscilla, 1979. "A bivariate stable characterization and domains of attraction," Journal of Multivariate Analysis, Elsevier, vol. 9(2), pages 206-221, June.
    7. 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.
    8. Kozubowski Tomasz J., 1997. "Characterization Of Multivariate Geometric Stable Distributions," Statistics & Risk Modeling, De Gruyter, vol. 15(4), pages 397-416, April.
    9. S. T. Rachev & A. SenGupta, 1993. "Laplace-Weibull Mixtures for Modeling Price Changes," Management Science, INFORMS, vol. 39(8), pages 1029-1038, August.
    10. 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.
    11. Tomasz J. Kozubowski & Krzysztof Podgórski, 2000. "A Multivariate and Asymmetric Generalization of Laplace Distribution," Computational Statistics, Springer, vol. 15(4), pages 531-540, December.
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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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