The approximations of the ruin probability in classical risk model (Q2740091)

The paper deals with approximated evaluations of the ruin probability in the classical risk model. The author gives the description of the classical risk model and the corresponding Cramér-Lundberg approximation and the inequality for the ruin probability. Then Beekman-Bowers approximation, De Vylder approximation, diffusion approximation and comparison of these approximations are presented. For the comparison of the approximations the relative error of the approximation \(\varepsilon(u)=(\bar\psi (u)-\psi(u))/\psi(u)\) is applied. Here \(\psi(u)\) is the ruin probability, \(\bar\psi(u)\) is the corresponding approximation of the ruin probability. The practical applications of the ruin probability approximations for 30 Ukrainian insurance companies in the cases of exponential distribution and Gamma distribution of insurance payments are considered.