par Lefèvre, Claude ;Picard, Philippe
Référence Methodology and Computing in Applied Probability, 16, 4, page (885-905)
Publication Publié, 2014-10
Article révisé par les pairs
Résumé : Recently, Lefèvre and Picard (Insur Math Econ 49:512-519, 2011) revisited a non-standard risk model defined on a fixed time interval [0,t]. The key assumption is that, if n claims occur during [0,t], their arrival times are distributed as the order statistics of n i.i.d. random variables with distribution function Ft(s), 0 ≤ s ≤ t. The present paper is concerned with two particular cases of that model, namely when Ft(s) is of linear form (as for a (mixed) Poisson process), or of exponential form (as for a linear birth process with immigration or a linear death-counting process). Our main purpose is to obtain, in these cases, an expression for the non-ruin probabilities over [0,t]. This is done by exploiting properties of an underlying family of Appell polynomials. The ultimate non-ruin probabilities are then derived as a limit.