Ruin probability for discrete risk processes

TL;DR

This paper analyzes the ruin probability in discrete risk processes modeled by skip-free random walks, deriving crossing probabilities using ballot theorems, and extends the model with perturbations to generalize these results.

Contribution

It introduces a novel application of ballot theorems to discrete risk processes and extends the model to include perturbations, broadening the understanding of crossing probabilities.

Findings

Derived ruin probabilities for skip-free random walks.

Compared discrete and continuous risk process results.

Generalized crossing results to perturbed models.

Abstract

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.