On approximating the ruin probability when claim severity distribution is lognormal - Mihaela Iftimie (Chiru)

The calculation of the probability of ruin is one of the classical problems in actuarial science, the ruin probability being a good indicator of how the insurer manages its assets and liabilities. The purpose of the paper is to illustrate and compare different infinite time ruin probability approximations, studying a heavy-tailed claim size distribution (using MTPL’s line of business claims), namely the lognormal distribution. The case study highlights the results of the empirical analysis obtained by applying a set of approximation methods and also new approaches such as a simulation algorithm based on Pollaczeck-Khinchin formula and the use of the ruin probability in finite time to approximate the ruin probability in infinite time. The study is of increased significance in the following respects: (1) it can support people involved in decision-making process (such as risk managers, actuaries, company’s management) to take decisions and measures regarding the long-term stability of the lines of business; (2) is an analysis that brings new empirical results in the field, being based on real and recent data from the Romanian insurance market.