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On the first crossing of the surplus process with a given upper barrier

par Picard, Philippe ;Lefèvre, Claude
Référence Insurance. Mathematics & economics, 14, 2, page (163-179)
Publication Publié, 1994-05

Article révisé par les pairs

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Résumé :

In the classical model of risk theory with the claim sizes arithmetically distributed, we consider the time T of the first crossing between the surplus process and a given (non-necessarily linear) upper barrier. The distribution of T is recognized to be discrete and the related probabilities can be expressed explicitly using a family of Abel-Gontcharoff polynomials when all claims have unit value, or a natural extension of these polynomials in the general case. © 1994.