The Gerber-Shiu Expected Discounted Penalty Function: An Application to Poverty Trapping

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 Enqu^ete Multisectorielle Continue (EMC) 2014.