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Exemplification of Ruin Probabilities

The following numerical values of ruin probabilities, Ψ(u, T) for finite times T, have been calculated by the method proposed in “Analytical steps towards a numerical calculation of the ruin probability for a finite period when the risk process is of the Poisson type or of the more general type studied by Sparre Andersen”, presented to this colloquium by Olof Thorin. The notations used in the sequel follow those of Thorin. Two distributions of the individual claims are considered, viz., The latter distribution is a rather crude attempt to interprete the extremely skew distribution (Swedish non-industry fire insurance 1948-1951) considered by Cramér in his treatise “Collective Risk Theory”, Jubilee volume of Försäkringsaktiebolaget Skandia (1955) pp. 43-45. Likewise two distributions of the interoccurence times are considered, viz., The d.f.B was considered by Sparre Andersen (TICA 1957 vol. II pp. 225-227). Note that the first moment equals one in all the d.f. mentioned. Though the analytical machinery also seems to work for o ≤ c ≤ 1 the Ψ values are indicated only for some values of c > 1. As known from Thorin's paper c stands for 1 + λ, where λ is the premium loading, which means that for c = o Ψ(u, T) corresponds to the tail of the d.f. for the total amount of claims during the period (o, T).