  This work is entirely devoted to compare the largest claims from two
heterogeneous portfolios. It is assumed that the claim amounts in an insurance
portfolio are nonnegative absolutely continuous random variables and belong to
a general family of distributions. The largest claims have been compared based
on various stochastic orderings. The established sufficient conditions are
associated with the matrices and vectors of model parameters. Applications of
the results are provided for the purpose of illustration.

Risk Management;Probability