Ruin Probabilities for Risk Models with Ordered Claim Arrivals

Claude Lefèvre () and Philippe Picard ()
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Claude Lefèvre: Université Libre de Bruxelles
Philippe Picard: Université de Lyon

Methodology and Computing in Applied Probability, 2014, vol. 16, issue 4, 885-905

Abstract: Abstract 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 F t (s), 0 ≤ s ≤ t. The present paper is concerned with two particular cases of that model, namely when F t (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.

Keywords: Order statistics; (Mixed) Poisson process; Linear birth process with immigration; Linear death process; Ruin probability; Finite or infinite horizon; Appell polynomials; Primary 62P05; Secondary 60G40, 12E10 (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/s11009-013-9334-y

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