Reduced-bias estimator of the ruin probability in infinite time for heavy-tailed distributions with index in the upper half of the unit interval

In insurance companies, the ruin probability is considered as the one of the main risk measures developed in risk theory, and the problems of its calculation and approximation have attracted a lot of attention. Statistical estimation have been investigated on the ruin probability in infinite time for heavy-tailed insurance loses. However, these estimation suffer heavily from under-coverage or have a bias problem. We therefore need another method for estimating the probability of ruin in infinite time for heavy-tailed losses. This is why, in this paper, we propose a reduced-bias estimator for the ruin probability in infinite time for heavy-tailed distributions with an index in the upper half of the unit interval. Our approach is based on a reduced-bias estimator for this specific index in the context of heavy-tailed distributions. Additionally, we demonstrate the behavior of the proposed estimator and compare it to the classical estimator in terms of bias and mean squared error. The simulation results clearly show that our bias reduction methodology performs well.