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ESSEC Working Papers,
ESSEC Research Center, ESSEC Business School

No WP1417: An Extension of the Class of Regularly Varying Functions

Meitner Cadena () and Marie Kratz ()
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Meitner Cadena: UPMC (Université Pierre-et-Marie-Curie) à Paris 6 & CREAR (Center of Research in Econo-finance and Actuarial sciences on Risk) at ESSEC, Postal: 4 place Jussieu , 75005 Paris, FRANCE
Marie Kratz: ESSEC Business School, Postal: AVENUE BERNARD HIRSCH, CS 50105 CERGY, 95021 CERGY PONTOISE CEDEX, FRANCE

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.

Keywords: asymptotic behavior - domains of attraction; extreme value theory; Karamata’s representation theorem; Karamata’s theorem; Karamata’s tauberian theorem; measurable functions; von Mises’ conditions; Peter and Paul distribution; regularly varying function

JEL-codes: C12

35 pages, December 2014

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