Cramér-Lundberg results for the infinite time ruin probability in the compound binomial model

• Autor(a) principal: Sundt, Bjørn
• Data de Publicação: 2007
• Outros Autores: Reis, Alfredo D. Egídio dos
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10400.5/24470
• topic: Cramér - Lundberg Approximation; Ruin Approximation; Poisson Model

The compound binomial model for the risk process was introduced by Gerber (1988) and is sometimes considered as a discrete time approximation to the classical compound Poisson model in continuous time; Dickson (1994) discusses this issue. After having introduced some notation in Section 2, we describe the model and set up some recursions for the in nite time ruin probability in Section 3. The core of the paper is Section 4. Here we present the Lundberg inequality and the Cramér-Lundberg approximation for the infinite time ruin probability in the compound binomial model and characterise the class of severity distributions for which the asymptotic expression is exact. Finally, in Section 5, we compare this characterisation with the analogous characterisation in the continuous time Poisson model. Although it is well known in the latter model, we give a deduction comparable with the one in Section 4.