Ordering claim size distributions and mixed Poisson probabilities

Abstracts and Reviews model. r _~_ 074027 (M13) Some stable algorithms in ruin theory and their applications. Dickson D.C.M. (*), Egidio dos Reis A.D. (**), Waters H.R., The University of Melbourne (*), ISEG, Lisbon (* *), Heriot-Watt University, Edinburgh, Centre for Actuarial Studies, Research Paper, nr. 19, I995, pp. l-28. In this paper we present a stable recursive algorithm for the calculation of the probability of ultimate ruin in the classical risk model. We also present stable recursive algorithms for the calculation of the joint and marginal distributions of the surplus prior to ruin and the severity of ruin. In addition we present bounds for these distributions. Keywords: Probability of ruin, severity of ruin, surplus prior to ruin, recursive calculation, stable algorithm, compound binomial model. i.. 1M20: NUMERICAL ANALYSIS IN INSURANCE, GENERAL AND MISCELLANEOUS 074028 (M20) Experimental design for non-linear problems. Sebastiani P. (*), Settimi R., City University London (*), University of Perugia, Actuarial Research Paper Nr. 78, 1995, pp. I-13. The paper presents new results on the choice of the experiment in some non-linear situations, characterized by an information matrix which assumes a particular form. A minimal design is proved to be optimal for a variety of models and some examples are considered. An alternative way based on a numerical procedure is presented to find optimal &signs when the number of experimental trials is small. An investigation on the robustness is carried out to check the sensitivity of the locally D-optimal design with respect to a poor initial guess of the parameters. Keywords: Generalized Linear Models, locally optimal designs, D-optimal& ef$ciency, Monte-Carlo.

M21: GRADUATION 074029 (M21) Graduation by Kernel and adaptive kernel methods with a boundary correction.

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Gavin J. (*), Haberman S., VerrallR. (**), University of Bath, England (*), City University, London (* *),Transactions of the society of actuaries, Vol.&VII, Preprint I, 1995, pp. I-37. This paper explores the flexibility of kernel estimation as a means of nonparametric graduation and relates it to moving-weighted-average graduation. Our primary objective is to focus attention on a model that makes explicit allowance for the variation in exposure over age. We also consider various transformations of the data, cross-validation as an objective method for choosing the smoothing parameter, and diagnostic methods for checking assumptions. A kernel function for improving the estimate at a boundary is discussed, and the results are applied to two mortality tables. Keywords: Graduation.

M30: PREMIUM, PREMIUM PRINCIPLES, ORDERING OF RISKS 074030 (M30) Ordering claim size distributions and mixed Poisson probabilities. Kaas R. (*), Hesselager O., University of Amsterdam, The Netherlands (*), University of Copenhagen, Denmark, Working Paper, nr. 133, 1995, pp. I-14. We investigate various orderings between continuous distributions for severities, having the same first n moments. Such situations occur for instance when severity distributjons are fitted by the method of moments. General results are derived which establish an ordering between such distributions, and these results are applied to compare the Gamma, the Inverse Gauss and the lognormal distributions with equal means and variances. Finally, we consider the situation where such continuous distributions are used as mixing distributions in mixed Poisson models for claim numbers, and show that the order properties of the mixing distributions are inherited by the corresponding mixed Poisson distributions. Keywords : Ordering, Mixed Poisson Distribution 074031 (M30) On a class of premium principles including the Esscher principle. Kamps U., University of Dortmund, Forschungsbericht 95/4, 1995, pp. I-8. A class of premium calculation principles is considered with the premiums obtained as expected