  We study the discrete time risk process modelled by the skip-free random walk
and we derive the results connected to the ruin probability, such as crossing
the fixed level, for this kind of process. We use the method relying on the
classical ballot theorems to derive these results and compare them to the
results obtained for the continuous time version of the risk process. We
further generalize this model by adding the perturbation and, still relying on
the skip-free structure of that process, we generalize the previous results on
crossing the fixed level for the generalized discrete time risk process.
