An identity based on the generalised negative binomial distribution with applications in ruin theory
-
Published:2018-09-10
Issue:2
Volume:13
Page:308-319
-
ISSN:1748-4995
-
Container-title:Annals of Actuarial Science
-
language:en
-
Short-container-title:Ann. actuar. sci.
Author:
Dickson David C. M.
Abstract
AbstractIn this study, we show how expressions for the probability of ultimate ruin can be obtained from the probability function of the time of ruin in a particular compound binomial risk model, and from the density of the time of ruin in a particular Sparre Andersen risk model. In each case evaluation of generalised binomial series is required, and the argument of each series has a common form. We evaluate these series by creating an identity based on the generalised negative binomial distribution. We also show how the same ideas apply to the probability function of the number of claims in a particular Sparre Andersen model.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,Economics and Econometrics,Statistics and Probability
Reference15 articles.
1. The time to ruin and the number of claims until ruin for phase-type claims;Frostig;Insurance: Mathematics and Economics,2012
2. Aspects of Risk Theory
3. Joint densities involving the time to ruin in the Sparre Andersen risk model under exponential assumptions;Landriault;Insurance: Mathematics and Economics,2011
4. Mathematical Fun with the Compound Binomial Process