The moments of ruin time in the classical risk model with discrete claim size distribution

✍ Scribed by Philippe Picard; Claude Lefèvre

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 544 KB
• Volume: 23
• Category: Article
• ISSN: 0167-6687
• DOI: 10.1016/s0167-6687(98)00025-0

✦ Synopsis

Firstly exact simple expressions are given for the moments Mr = Eo(Trl{T<~}) when the initial reserves are equal to zero. Then for positive initial reserves the same moments are expressed very compactly through the Mr's, and the polynomials e,~(O = eXtP(St = n), n = 0, 1 .... In both cases the results are exact and valid for any arithmetic claim size distribution. Our main tool is the generalized Appell structure of the polynomials family {en, n ~ N}. Both cases