DOI: 10.1515/demo-2023-0107 ISSN: 2300-2298

Abel-Gontcharoff polynomials, parking trajectories and ruin probabilities

Claude Lefèvre, Philippe Picard
  • Applied Mathematics
  • Modeling and Simulation
  • Statistics and Probability


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.

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