The Paris Agreement reached during the COP21 in December 2015 represents a timid step towards burden sharing in emission mitigation involving all countries. However, given the heterogeneity of countries and their relative differences in vulnerability to climate change damage and in mitigation costs, compensating schemes are required to reach an effective agreement. This paper investigates the role of the Green Climate Fund (GCF) as a potential compensating measure for both adaptation and mitigation actions under a global climate regime. A dynamic climate-economy computable general equilibrium model (GDynEP) is developed by including both a monetary valuation of climate change damage costs and two alternative methods to determine the allocation of GCF resources among receiving countries and between adaptation and mitigation contributions. Results show that, despite the high costs associated with the implementation of mitigation actions, most developing countries would face even higher costs in case of inaction. Furthermore, the preference of a country for an allocation method is strongly influenced by its characteristics and needs. Consequently, a main policy conclusion is to design country-specific sharing rules for GCF in order to maximize country participation in a global agreement.