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In this paper, the task of increasing the accuracy of net premium estimations in non-life insurance is considered. Improvements are achieved by involving additional information about a known quantile of loss cumulative distribution function. The additional information is used by projection the empirical cumulative distribution function onto the class of cumulative distribution functions with a certain quantile, and then the modifi ed empirical cumulative distribution function is substituted into the integral that yields the mean value. This allows us to obtain a modifi ed estimation of mean value using additional information about the quantile which is unbiased and its variance is asymptotically less than the variance of the classical sample mean, so that the mean-square error of the modifi cation is also smaller. Therefore, the modifi ed estimation is more accurate than the classical one for a large sample size. The infl uence of a quantile value on the variance of the new estimation is studied for uniform, triangular and normal distributions. It is suggested that the minimum of the variance is reached when a known quantile is equal to the median (symmetry center) for symmetrical distribution. Based on Simpson triangular distribution, it was shown that for cases of skewed distributions involving the quantile allows one to decrease the variance more signifi cantly than for symmetrical ones. The modifi ed estimation of mean value is applied to a real data set for calculation of a net premium. The data contain information about payments for voluntary health insurance of some insurance company. It is demonstrated that the classical method underestimates the net premium, and so it could lead to the company’s bankruptcy. After applying the new modifi ed technique, the net premium becomes higher and the bankruptcy risk is reduced as well. This paper contains practically signifi cant results which make it possible to give important recommendations to an insurance company. MATHEMATICAL METHODS AND ALGORITHMS OF BUSINESS INFORMATICS

Estimating the net premium using additional information about a quantile of the cumulative distribution function