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