# Teorija povjerenja

Poljak, Mihaela (2014) Teorija povjerenja. Diploma thesis, Faculty of Science > Department of Mathematics.

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## Abstract

In this thesis we deal with determining the precise individual risk premium. Since the competition in the market is high, the goal of every insurance company is to offer the most accurate premium for each risk. Premiums should not be too high because that can refuse customers, on the other hand premiums should not be too low because the insurance company needs to gather enough funds to fulfill obligations to their clients. Individual premium is based on individual claims data in prior periods. Here we come to the problem of how to estimate premium for the insured who is in the insurance for a short period of time or a new insured. In this case, the premium can better estimate the average damage similar to insurance risk. We called it the collective premium. It is good for the insured who is entirely new, but it is clear that for other insured premium it should depend on the individual and the collective premium. We have shown that the best estimate of the premium is Bayesian premium that depends on the behavior of individuals and the average behavior of similar risk. However, the Bayesian estimator is often complicated to calculate exactly. Moreover, in order to calculate the Bayesian estimator we have to specify the conditional distribution as well as the a priori distribution for damage, which, in practice, can often neither be inferred from any given data nor guessed by intuition. So instead the Bayesian estimator we look for the best estimator in the class of all linear estimator functions of our sample and such estimators are called credibility estimators. Credibility estimators have convex form as combinations of the average value of the individual risk data and average value of the entire collective data. The question is, which of these two variables affects the premium more, this question is a subject in credibility theory. If the sample of data is larger, premiums will be closer to the average value of the individual risk data, and for smaller sample premium will be closer to the average value of the whole collective data.

Item Type: Thesis (Diploma thesis) Huzak, Miljenko 2014 63 NATURAL SCIENCES > Mathematics Faculty of Science > Department of Mathematics Iva Prah 17 Jun 2015 11:24 17 Jun 2015 11:24 http://digre.pmf.unizg.hr/id/eprint/4056

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