A note on ruin problems in perturbed classical risk models

TL;DR

This paper derives explicit formulas for the joint densities of ruin time and claim count in perturbed classical risk models, aiding in understanding risk processes with perturbations.

Contribution

It introduces new explicit formulas for joint densities in perturbed risk models using auxiliary processes, advancing risk analysis methods.

Findings

Explicit formulas for joint densities of ruin time and claim count

Enhanced understanding of perturbed risk process behavior

Methodology applicable to various risk model perturbations

Abstract

In this short note, we derive explicit formulas for the joint densities of the time to ruin and the number of claims until ruin in perturbed classical risk models, by constructing several auxiliary random processes.