Comparison of ruin probability estimates in the presence of heavy tails
This paper deals with the estimation of the ruin probability in the presence of heavy tails, in a framework in which the claim size distribution is a Pareto one. For this purpose, four methods are presented. The first one, due to Embrechts and Veraverbeke, gives an asymptotic expression for the ruin probability when the initial surplus tends to infinity; the second one, due to Goovaerts and De Vylder, consists in an algorithm that provides two-sided bounds of the ruin probability, obtained by solving the renewal equation through discretization. This method appears particularly suitable in case of small initial capital. By means of the third method, proposed by Willmot and extended by Kalashnikov, it is possible to obtain an upper bound for the ruin probability by means of so-called test functions. By the fourth method, proposed by Kalashnikov, two-sided bounds for the ruin probability are obtained using truncation of random variables. The theoretical treatment is supported by numerical results.
scientific article; zbMATH DE number 1295570
scientific article