Approximations of the ruin probability in a discrete time risk model
Volume 7, Issue 3 (2020), pp. 221–243
Pub. online: 4 August 2020
Type: Research Article
Open Access
Open Access
Received
2 June 2020
2 June 2020
Revised
18 July 2020
18 July 2020
Accepted
18 July 2020
18 July 2020
Published
4 August 2020
4 August 2020
Abstract
Based on a discrete version of the Pollaczeck–Khinchine formula, a general method to calculate the ultimate ruin probability in the Gerber–Dickson 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.
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