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

TL;DR

This paper establishes functional weak laws for weighted mean loss or gain statistics, enabling comprehensive temporal and spatial risk analysis across various fields like finance and medicine.

Contribution

It introduces time-dependent and uniform weak asymptotic laws for WMLG statistics, including UTH and LTH types, with applications to risk measurement and comparison.

Findings

Derived weak asymptotic laws for WMLG statistics

Applied results to Kakwani and Shorrocks indices

Provided data-driven applications with pseudo-panel data

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.