Risk models in insurance and epidemics: a bridge through randomized polynomials

The purpose of this work is to construct a bridge between two classical topics in applied probability: the finite-time ruin probability in insurance and the final outcome distribution in epidemics. The two risk problems are reformulated in terms of the joint right-tail and left-tail distributions of order statistics for a sample of uniforms. This allows us to show that the hidden algebraic structures are of polynomial type, namely Appell in insurance and Abel-Gontcharoff in epidemics. These polynomials are defined with random parameters, which makes their mathematical study interesting in itself.SCOPUS: ar.j