Based on classical asymptotic theory for recurrence equations, the concept of local stability at infinity is introduced. It extends the results of Panjer and Wang (1993). To bridge the gap between the local range at infinity and the global range of interest, some practical methods of stability checking are proposed. Applications are found in the recursive evaluation of the mixed Poisson distributions with beta or transformed beta mixing densities, the P6lya-Aeppli distribution and the Delaporte distribution. Keywords: Beta-Distribution. Stability.
073021 (M22) An Improved Recursion for the Compound Generalized Poisson Distribution. Sharif A.H., Panjer H.H., Mitteilungen der schweizerische Vereinigung der Versicherungsmathematiker, 1995, Heft I, pp . 93-98 .
Goovaerts and Kaas (199 I) gave a two step recursive scheme to evaluate compound generalized Poisson distributions. In this paper, their recursive scheme is improved and more general results are proposed. Keywords: Recursive Calculation.
073022 (M22) A Fuzzy Expert System for Evaluation of Municipalities - an Application. Hellman A., Finland, Transactions ICA Brussels, 1995. Vol. 1, pp. /59-188. Fuzzy modelling has some advantages and also some disadvantages. A very clear advantage is that we can create a model of a situation based almost totally only on subjective knowledge not very easily written into figures. It is obvious that such a model is not accurate - but then the whole problem is in such cases usually not accurate. Also such a model is, of course, subjective. But, again, a view of an expert is, although subjective, considered to be also best knowledge on the subject, hence the subjectivity may not be a disadvantage. In several fields a traditional, accurate model is the best. What fuzzy modelling has and the traditional, for example risk theoretical modelling, has not, is an ability to make models always simple enough for everyday use and almost everybody's understanding. Naturally this is due to some lack in accuracy, a disadvantage always presents with fuzzy modelling. In fact, fuzzy modelling is means to use especially in situations when accurate absolute values are not necessary, or cannot be reached. In probabilistic areas fuzzy techniques are not perhaps usually the wisest solution: there we have already very
strong mathematical theory for problem solving. Hence fuzzy modelling or fuzzy set theory in general may not be an answer for tariff building or interest estimation or other areas where actuarial mathematics has already developed efficient and accurate tools. For actuarial work, however, fuzzy modelling brings an excellent tool to solve problems like customer evaluation or allocation of marketing efforts. Also a bonus-malus tariff based on many parameters would be a possible application for a fuzzy expert system - not as a tariff calculator, but for giving a rating as a basis of a premium decision. On the whole, as a tariff basis it would not be unwise to run the register of a customer through an evaluating expert system before deciding on bonuses or discount. The ability to take into account many different features with emphasis on the important parameters just of the amount assumed correct, and to produce from that a single evaluation as an outcome is an undeniable benefit of fuzzy expert systems. As any expert systems, also fuzzy expert systems must always be used only as helpful tools. As an addition to one's own judgment or to the knowledge already at hand, however, a fuzzy expert system can provide us with first class extra information. On the whole the important features in using fuzzy modelling are the following: The models can be easily modified to new and changed situations. The smooth basic functions give continuity to the values of the model which otherwise, using more traditional fuzzy set methods, perhaps would not be obtained. In the same way as the modifying of the model is easy, also adding new fuzzy features to an existing model can be done with no big difficulties. Keywords : Fuzzy Set Methods, Expert Systems.
M30: PREMIUM, PREMIUM PRINCIPLES,
ORDERING OF RISKS 073023 (M30) Guaranteed Renewability in Insurance. Pauly M.V., Kunreuther H., Hirth R.,Jollrnal of Risk and Uncertainty 1995, Vol. 10, number 2, pp . 143-156. We propose a guaranteed renewability (GR) insurance in which a sequence of premiums would enable insurers to break even and would be chosen by both low- and high-risk buyers, whether or not they had suffered a loss. The premium schedule would continually decline over time, as the insurer collects more information to determine who the low-risk buyers are. The highest