Paper: arXiv 2402.11715

Authors: José Miguel Flores-Contró

Abstract

In this article, we consider a risk process to model the capital of a household. Our work focuses on the analysis of the trapping time of such a process, where trapping occurs when a household’s capital level falls into the poverty area. A function analogous to the classical Gerber-Shiu function is introduced, which incorporates information on the trapping time, the capital surplus immediately before trapping and the capital deficit at trapping. We derive, under some assumptions, a model belonging to the family of generalised beta (GB) distributions that describes the distribution of the capital deficit at trapping given that trapping occurs. Affinities between the capital deficit at trapping and a class of poverty measures, known as the Foster-Greer-Thorbecke (FGT) index, are presented. The versatility of this model to estimate FGT indices is assessed using household microdata from Burkina Faso’s Enquête Multisectorielle Continue (EMC) 2014.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 6.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper innovatively applies the Gerber-Shiu risk theory framework from actuarial science to socioeconomic poverty dynamics. It combines heavy stochastic calculus and analytical derivations with empirical microdata validation from Burkina Faso.

Research Flowchart

  flowchart TD
    A[Goal: Model Household Poverty Trapping via Gerber-Shiu Risk Theory] --> B[Introduce Gerber-Shiu Function for Capital Trapping Time & Deficit]
    B --> C[Derive Generalised Beta Distribution for Capital Deficit at Trapping]
    D[Input: Household Microdata EMC 2014 Burkina Faso] --> E[Estimate Foster-Greer-Thorbecke Poverty Indices]
    C --> E
    E --> F[Outcome: Versatile Actuarial Framework for Quantifying Poverty Dynamics]

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0 of 61 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.