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An Extension of the Class of Regularly Varying Functions

Author

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  • Meitner Cadena

    (UPMC - Université Pierre et Marie Curie - Paris 6, ESSEC Business School)

  • Marie Kratz

    (ESSEC Business School, MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5 - UPD5 - Université Paris Descartes - Paris 5 - INSMI-CNRS - Institut National des Sciences Mathématiques et de leurs Interactions - CNRS Mathématiques - CNRS - Centre National de la Recherche Scientifique)

Abstract

We define a new class of positive and Lebesgue measurable functions in terms of their asymptotic behavior, which includes the class of regularly varying functions. We also characterize it by transformations, corresponding to generalized moments when these functions are random variables. We study the properties of this new class and discuss their applications to Extreme Value Theory.

Suggested Citation

  • Meitner Cadena & Marie Kratz, 2014. "An Extension of the Class of Regularly Varying Functions," Working Papers hal-01097780, HAL.
    • Handle: RePEc:hal:wpaper:hal-01097780
    Note: View the original document on HAL open archive server: https://essec.hal.science/hal-01097780
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    References listed on IDEAS

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    1. Hadar, Josef & Russell, William R., 1971. "Stochastic dominance and diversification," Journal of Economic Theory, Elsevier, vol. 3(3), pages 288-305, September.
    2. Daley, D.J. & Goldie, Charles M., 2006. "The moment index of minima (II)," Statistics & Probability Letters, Elsevier, vol. 76(8), pages 831-837, April.
    3. de Haan, L. & Resnick, S. I., 1981. "On the observation closest to the origin," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 301-308, August.
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    Cited by:

    1. Wei Jiang & Steven Kou, 2021. "Simulating risk measures via asymptotic expansions for relative errors," Mathematical Finance, Wiley Blackwell, vol. 31(3), pages 907-942, July.

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