Approximations of the ruin probability in a discrete time risk model
Abstract
Based on a discrete version of the PollaczeckKhinchine formula, a general method to calculate the ultimate ruin probability in the GerberDickson risk model is provided when claims follow a negative binomial mixture distribution. The result is then extended for claims with a mixed Poisson distribution. The formula obtained allows for some approximation procedures. Several examples are provided along with the numerical evidence of the accuracy of the approximations.
 Publication:

arXiv eprints
 Pub Date:
 June 2020
 DOI:
 10.48550/arXiv.2006.01391
 arXiv:
 arXiv:2006.01391
 Bibcode:
 2020arXiv200601391S
 Keywords:

 Mathematics  Probability;
 91B30
 EPrint:
 24 pages, 4 figures