Reinsurance mathematics is quite an old field of Mathematical Risk Theory.All traditional
reinsurance treaties were analysed mathematically in many papers. So one can find a nice
theory on the stoploss cover in [1]. The author himself developed a comprehensive theory for
generalizations of the classical largest claims reinsurance cover. For an introduction on this
see [5]. In one pioneering paper he had an even more generalized treaty under investigation
(see [2]). He called those treaties reinsurance treaties based on ordered claims. The question
arises if there is a practical reinsurance treaty based on ordered claims that does not fit into
the author’s comprehensive theory of generalized largest claims reinsurance covers (see
again [5]). Fortunately there is one. It is the so-called drop down excess of loss cover. What
about the premium for this? This question is treated with in detail in the present paper.