On the asymptotic behavior of insurance company reserve in the case of random number of clients

The paper considers the asymptotic behavior of the average total losses of an organization at risk in the case when the number of factors leading to the loss is random. An asymptotic comparison of the activities of such organizations is carried out in terms of the necessary additional number of such factors. Two examples illustrating the results are considered. The first example concerns a truncated binomial distribution, while the second example considers a truncated Poisson distribution. These distributions describe the number of random factors that lead to losses.