Burr’s Distribution for Asymptotic Studies of the Behavior of an Insurance Company’s Reserve

Asymptotic behavior of the reserve of an organization exposed to risk is considered for when the number of factors leading to a loss is random. A specific distribution of losses (the Burr distribution) is considered. The activities of these organizations are compared asymptotically in terms of the required additional number of such factors. Two examples are given to illustrate the obtained results. The first example is related to the maximum loss; the second considers truncated binomial and Poisson distributions that describe the number of random factors leading to losses.