The probability of ruin
The author proposes explicit solutions of the ruin probability problem in the case of the classical risk model. He gives exact formulas for the \(\varphi\left(u\right)\) (probability of no ruin on the infinite time interval with the initial surplus \(u\)) in the case where the distribution function of individual claim \(F\left(x\right)\) is of the hyperexponential type, is the Erlang distribution, is a mixture of the exponential and the generalized binomial distribution. For the discrete distributions the author proposes formulas for determining \(\varphi\left(u\right)\) in the case of Poisson distribution, negative binomial distribution, geometrical distribution, and logarithmic distribution.
scientific article; zbMATH DE number 1631963