On the Ruin Probabilities for a General Perturbed Renewal Risk Process

Abstract. 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.