Abel-Gontcharoff polynomials, parking trajectories and ruin probabilities

Lefèvre Claude () and Picard Philippe
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Lefèvre Claude: Département de Mathématique, Université Libre de Bruxelles, Campus de la Plaine C.P. 210, B-1050 Bruxelles, Belgium
Picard Philippe: Université de Lyon 1, Institut de Science Financière et d’Assurances, 50 avenue Tony Garnier, F-69366 Lyon Ceeedex 07, France

Dependence Modeling, 2023, vol. 11, issue 1, 17

Abstract: The central mathematical tool discussed is a non-standard family of polynomials, univariate and bivariate, called Abel-Goncharoff polynomials. First, we briefly summarize the main properties of this family of polynomials obtained in the previous work. Then, we extend the remarkable links existing between these polynomials and the parking functions which are a classic object in combinatorics and computer science. Finally, we use the polynomials to determine the non-ruin probabilities over a finite horizon for a bivariate risk process, in discrete and continuous time, assuming that claim amounts are dependent via a partial Schur-constancy property.

Keywords: remarkable polynomials; parking functions; ruin probability; partial Schur-constancy (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:vrs:demode:v:11:y:2023:i:1:p:17:n:1012

DOI: 10.1515/demo-2023-0107

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