This work considers the European Resource Adequacy Assessment, which is a pan-European resource adequacy process that is being developed by the European Networks of Transmission System Operators for Electricity (ENTSO-E). A critical part of this process is the so-called Economic Viability Assessment model, which aims at determining future expansion and retirement capacity opportunities for the entire European network. As such, the problem is stochastic. Nevertheless, due to computational constraints, simplified approaches have been followed by ENTSO-E. Our work formulates the problem as a two-stage stochastic problem and proposes two decomposition algorithms for solving the problem which are implemented in a high-performance computing infrastructure. The first is a subgradient-based algorithm, and the second uses a relaxation of the second stage (the economic dispatch) in order to speed up the subgradient calculation thus achieving a considerable reduction in solution time. We compare our schemes against the commonly used Bender's decomposition. We compare the obtained stochastic solution against the deterministic solution proposed by ENTSO-E for their 2021 study and analyze the impact of the stochastic solution on various adequacy indicators.