Approximations of the ruin probability in a discrete time risk model
David J. Santana, Luis Rincon
TL;DR
This paper develops a method to approximate the probability of ruin in a discrete risk model with claims following mixed distributions, providing formulas, examples, and numerical validation.
Contribution
It introduces a general approach to approximate ruin probabilities using a discrete Pollaczeck-Khinchine formula for mixed claim distributions.
Findings
The method accurately approximates ruin probabilities.
Numerical examples demonstrate the effectiveness of the approach.
Extensions to mixed Poisson claims are provided.
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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