Abel-Gontcharoff polynomials, parking trajectories and ruin probabilities
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 be...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2023-11-01
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| Series: | Dependence Modeling |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/demo-2023-0107 |
| _version_ | 1797405107679133696 |
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| author | Lefèvre Claude Picard Philippe |
| author_facet | Lefèvre Claude Picard Philippe |
| author_sort | Lefèvre Claude |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T03:05:57Z |
| format | Article |
| id | doaj.art-67b82a141b294fb9bdcb184c4fa9f1a7 |
| institution | Directory Open Access Journal |
| issn | 2300-2298 |
| language | English |
| last_indexed | 2024-03-09T03:05:57Z |
| publishDate | 2023-11-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Dependence Modeling |
| spelling | doaj.art-67b82a141b294fb9bdcb184c4fa9f1a72023-12-04T07:59:29ZengDe GruyterDependence Modeling2300-22982023-11-0111112110.1515/demo-2023-0107Abel-Gontcharoff polynomials, parking trajectories and ruin probabilitiesLefèvre Claude0Picard Philippe1Département de Mathématique, Université Libre de Bruxelles, Campus de la Plaine C.P. 210, B-1050 Bruxelles, BelgiumUniversité de Lyon 1, Institut de Science Financière et d’Assurances, 50 avenue Tony Garnier, F-69366 Lyon Ceeedex 07, FranceThe 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.https://doi.org/10.1515/demo-2023-0107remarkable polynomialsparking functionsruin probabilitypartial schur-constancy26c0505a9991b30 |
| spellingShingle | Lefèvre Claude Picard Philippe Abel-Gontcharoff polynomials, parking trajectories and ruin probabilities Dependence Modeling remarkable polynomials parking functions ruin probability partial schur-constancy 26c05 05a99 91b30 |
| title | Abel-Gontcharoff polynomials, parking trajectories and ruin probabilities |
| title_full | Abel-Gontcharoff polynomials, parking trajectories and ruin probabilities |
| title_fullStr | Abel-Gontcharoff polynomials, parking trajectories and ruin probabilities |
| title_full_unstemmed | Abel-Gontcharoff polynomials, parking trajectories and ruin probabilities |
| title_short | Abel-Gontcharoff polynomials, parking trajectories and ruin probabilities |
| title_sort | abel gontcharoff polynomials parking trajectories and ruin probabilities |
| topic | remarkable polynomials parking functions ruin probability partial schur-constancy 26c05 05a99 91b30 |
| url | https://doi.org/10.1515/demo-2023-0107 |
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