Smirnov, 1949, derived four limit types of distributions for linearly normalized central order statistics, under the weak convergence. In this paper, we investigate the asymptotic behavior of central order statistics under monotone normalization. The explicit forms of the limit distributions are obtained using regular norming sequences of mappings from the group of max-automorphisms and the solutions are found of two functional equations which characterize the possible nondegenerate limit of the k-th upper order statistic with central rank. The contribution to reinsurance is presented as a direct application of the k-th central order statistic in rensurance of the k-th largest claim, or reinsurance of the aggregate amount of the k largest claims in the portfolio. Another view of the Pick over the treshold method is given using central order statistics.