On the ruin probabilities for a general perturbed renewal risk process

This paper studies the ruin probabilities in a homogeneous continuous compound Poisson risk model which is adapted for the perturbed insurance risk model with standard Brownian motion. In such a model, we construct a martingale in terms of a differentiable exponential function based on the discounted and perturbed surplus process. We obtain the exponential upper bounds for the ruin probabilities using Martingale approach and provide a sharper exponential upper bound for the infinite time ruin probability. Moreover, we derive two asymptotic approximation formulas for the finite time ruin probability when claim size distribution belongs to some heavy -tailed families. Finally, several numerical examples are presented to show the effect of constant force of interest on the ruin probabilities and that our results are excellent and reliable.(c) 2023 Elsevier B.V. All rights reserved.

Automated summary

This paper examines the ruin probabilities in a homogeneous continuous compound Poisson risk model that is applicable to perturbed insurance risk models with standard Brownian motion. By constructing a martingale based on the discounted and perturbed surplus process, we establish exponential upper bounds for the ruin probabilities using the Martingale approach. Additionally, we derive two asymptotic approximation formulas for the finite time ruin probability when the claim size distribution belongs to heavy-tailed families. Numerical examples are presented to illustrate the impact of constant force of interest on the ruin probabilities, and the results are found to be excellent and reliable.