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Functional weak laws for the weighted mean losses or gains and applications

Authors
  • Lo, Gane Samb
  • Sall, Serigne Touba
  • Mergane, Pape Djiby
Type
Preprint
Publication Date
May 21, 2014
Submission Date
Jun 23, 2013
Identifiers
arXiv ID: 1306.5431
Source
arXiv
License
Yellow
External links

Abstract

We show in this paper that many risk measures arising in Actuarial Sciences, Finance, Medicine, Welfare analysis, etc. are garthered in classes of Weighted Mean Loss or Gain (WMLG) statistics. Some of them are Upper Threshold Based (UTH) or Lower Threshold Based (LTH). These statistics may be time-dependent when the scene is monitored in the time and depend on specific functions $w$ and $d$. This paper provides time-dependent and uniformly functional weak asymptotic laws that allow temporal and spatial studies of the risk as well as comparison between statistics in terms of dependence and mutual influence. The results are particularised for usual statistics of that kind such that the Kakwani and Shorrocks ones. Datadriven applications based on pseudo-panel data are provided.

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