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Aix-Marseille Université
Institut de Mathématiques de Marseille (I2M) - UMR 7373
Site Saint-Charles : 3 place Victor Hugo, Case 19, 13331 Marseille Cedex 3
Site Luminy : Campus de Luminy - Case 907 - 13288 Marseille Cedex 9

Polynomial, order statistics and risk models in insurance and epidemics




Date(s) : 25/09/2017   iCal
14h00 - 15h00

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.

http://homepages.ulb.ac.be/~clefevre/

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