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RISK MODELS IN INSURANCE AND EPIDEMICS: A BRIDGE THROUGH RANDOMIZED POLYNOMIALS

Published online by Cambridge University Press:  23 March 2015

Claude Lefèvre  and
Philippe Picard
Claude Lefèvre
Affiliation:
Université Libre de Bruxelles, Département de Mathématique, Campus de la Plaine C.P. 210, B-1050 Bruxelles, Belgium E-mail: [email protected]
Philippe Picard
Affiliation:
Université de Lyon, Institut de Science Financière et d'Assurances, 50 Avenue Tony Garnier, F-69007 Lyon, France E-mail: [email protected]
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Abstract

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.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 29 , Issue 3 , July 2015 , pp. 399 - 420
Copyright
Copyright © Cambridge University Press 2015 

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