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 &gt; 1. As known from Thorin's paper c stands for 1 + λ, where λ is the premiumloading, 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).</jats:p

Calculation of Ruin Probabilities when the Claim Distribution is Lognormal

In this paper some ruin probabilities are calculated for an example of a lognormal claim distribution. For that purpose it is shown that the lognormal distribution function, Λ(y), may be written in the formwhere V(x) is absolutely continuous and without being a distribution function preserves some useful properties of such a function.An attempt is also made to give an approximant Λα(y) to Λ(y) such that Λα(y) is a linear combination of a low number of exponential distributions. For comparison, ruin probabilities are also calculated for two examples of Λα(y).In the considered numerical cases it is assumed that the occurrence of claims follows a Poisson process.</jats:p

Numerical evaluation of ruin probabilities for a finite period

In this paper the authors remind of the known formulas for the double Laplace-Stieltjes transforms of the ruin probabilities ψ(u, t), where u is the initial risk reserve and t stands for the operational time, in the case of independent interoccurence times and claim amounts such that the interoccurrence times are identically distributed Κ(t), t ≥ o, Κ(o) = o, and the claim amounts are identically distributed P(y), — ∞ &lt; y &lt; ∞. For some cases, where I — P(y) and I — Κ(t) are exponential polynomials, numerical inversions of the said Laplace-Stieltjes transforms are made for a selection of u- and t-values in combination with safety loadings of various sizes and signs. Moreover, some values are given when I — P(y) or I — Κ(t) are of Pareto type and comparisons are made with the results when the Pareto distributions are approximated by suitable exponential polynomials.</jats:p

Effect of vesicoureteral reflux on renal function in children with recurrent urinary tract infections

Effect of vesicoureteral reflux on renal function in children with recurrent urinary tract infections. The functional damage caused by vesicoureteral reflux (VUR) has been examined by unilateral clearance studies in 22 children with recurrent urinary tract infection (UTI) and representing 23 kidneys with large VUR, 7 kidneys with small to moderate VUR and 14 kidneys without VUR. Inulin clearance, Na+ excretion and glucose reabsorption were determined. In kidneys without or with small and moderate VUR, UTI had no effect on renal function if treated. In kidneys with large VUR extending into the pelvis and dilating the ureter, there was a gradual deterioration of glomerular filtration rate (GFR) that was accelerated after the age of 6yr. Before puberty more than 50% of renal function was lost despite strict medical care of the UTI. If this functional loss was unilateral, hyperfunction of the contralateral kidney was generally observed. Maximal glucose reabsorption was depressed in proportion to GFR. In kidneys with unilaterally low GFR, the fractional Na+ excretion was consistently increased as compared to the contralateral kidney with normal GFR. This adaptive increase in Na+ excretion must therefore be of intrarenal origin.Effet du reflux vésico-urétéral sur la fonction chez l'enfant atteint d'infection urinaire récidivante. L'altération de la fonction rénale déterminée par le reflux vésico-urétéral (VUR) a été étudiée par clearance unilatérale chez 22 enfants atteints d'infection urinaire récidivante (UTI). L'étude a porté sur 23 reins avec reflux importants, 7 reins avec reflux minime ou moyen et 14 reins sans reflux. La clearance de l'inuline, l'excrétion de Na et la réabsorption de glucose ont été déterminés. L'infection urinaire récidivante n'a pas d'effets sur la fonction des reins sans reflux ou avec reflux minime ou moyen. Dans les reins avec reflux important atteignant le bassinet et dilatant l'uretère on observe une détérioration progressive de la filtration glomérulaire, détérioration qui est plus rapide après l'âge de 6 ans. Avant la puberté, plus de 50% de la fonction rénale sont perdus malgré un traitement strict de l'infection urinaire récidivante. Quand cette diminution de la fonction est unilatérale, une augmentation de la fonction controlatérale est habituellement observée. La réabsorption maximale de gluclose est diminuée en proportion du débit de filtration glomérulaire. L'excrétion fractionnelle de sodium par les reins dont la filtration glomérulaire est diminuée est nettement plus grande que celle du rein controlatéral dont la filtration glomérulaire est normale. Il semble donc que cette adaptation dans l'excrétion du sodium doive être d'origine intrarénale