English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, we adapt the classic Cram\'er-Lundberg collective risk theorymodel to a perturbed model by adding a Wiener process to the compound Poissonprocess, which can be used to incorporate premium income uncertainty, interestrate fluctuations and changes in the number of policyholders. Our study is partof a Master dissertation, our aim is to make a short overview and presentadditionally some new approximation methods for the infinite time ruinprobabilities for the perturbed risk model. We present four differentapproximation methods for the perturbed risk model. The first method is basedon iterative upper and lower approximations to the maximal aggregate lossdistribution. The second method relies on a four-moment exponential De Vylderapproximation. The third method is based on the first-order Pad\'eapproximation of the Renyi and De Vylder approximations. The last method is thesecond order Pad\'e-Ramsay approximation. These are generated by fitting one,two, three or four moments of the claim amount distribution, which greatlygeneralizes the approximations. We test the precision of approximations using acombination of light and heavy tailed distributions for the individual claimamount. We assess the ultimate ruin probability and present numerical resultsfor the exponential, gamma, and mixed exponential claim distributions,demonstrating the high accuracy of these four methods. Analytical and numericalmethods are used to highlight the practical implications of our findings.

Approximations to ultimate ruin probabilities with a Wienner process perturbation