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In this paper,we propose a new risk measure which is based on the Orlicz premium principle to characterize catastrophe risk premium.The intention is to develop a formulation strategy for Catastrophe Fund.The logarithm equivalent form of reinsurance premium is regarded as the retention of reinsurer,and the differential earnings between the reinsurance premium and the reinsurer's retention is accumulated as a part of Catastrophe Fund.We demonstrate that the aforementioned risk measure has some good properties,which are further confirmed by numerical simulations in R environment.