Title: Polynomials and risk models
Authors: Claude Lefevre - Universite Libre de Bruxelles (Belgium) [presenting]
Abstract: The goal is to exhibit the underlying algebraic polynomial structure in the study of stochastic risk models. This is highlighted for two different topics of applied probability: the probability of ruin in insurance theory and the final size distribution in epidemic modeling. The polynomials involved are of a similar but different nature. In insurance, they are of Appell type, while in epidemics, they are of Abel-Gontcharoff type. They can also depend on several variables to take into account effects of heterogeneity. The basic properties of both polynomial families are discussed and then used to analyze the two problems of interest.