Computing ruin probability and minimum initial capital by simulation

Abstract

In this paper, we propose a new approximation method to obtain the ruin probability by modifying the PollaczekKhinchin approximation. The proposed approximation is simpler and requires fewer assumptions than other methods mentioned in the literature. The results from a simulation study show that, in some cases, the proposed method gave better ruin probability values in terms of the overall deviation from the exact values. Insurance companies are interested in calculating the initial capital by using ruin probability and so, with this in mind, we applied the proposed method to estimate the minimum initial capital that must be reserved to ensure that the ruin probability does not exceed an acceptable quantity. To illustrate the performance of our approximation, we estimated the ruin probability and the minimum initial capital with real data from an insurance company.

Keywords

• risk theory
• surplus process
• claim process
• infinite time
• insurance