Polynomial, order statistics and risk models in insurance and epidemics

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Date(s) - 25/09/2017
14 h 00 min - 15 h 00 min

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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 randomized parameters, which makes their mathematical study interesting in itself. A multivariate extension of this work will be also briefly discussed. This is joint work with Philippe Picard, Université de Lyon, ISFA.


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