Interdependencies among land use systems resemble a complex network connected through demand–supply relationships. Disruption of this network may catalyse systemic risks affecting food, energy, water and environmental security (FEWES) worldwide. We describe the conceptual development, expansion and practical application of a stochastic version of the Global Biosphere Management Model (GLOBIOM), used to assess competition for land use between agriculture, bioenergy and forestry at regional and global scales. In the stochastic version of the model, systemic risks of various kinds are explicitly covered and can be analysed and mitigated in all their interactions. While traditional deterministic scenario analysis produces sets of scenario‐dependent outcomes, stochastic GLOBIOM explicitly derives robust outcomes that leave the systems better‐off, independently of which scenario applies. Stochastic GLOBIOM is formulated as a stochastic optimisation model that is critical for evaluating portfolios of robust interdependent decisions: ex‐ante strategic decisions (production allocation, storage capacities) and ex‐post adaptive (demand, trading, storage control) decisions. As an example, the model is applied to the question of optimal storage facilities, as buffers for production shortfalls, to meet regional and global FEWES requirements when extreme events occur. Expected shortfalls and storage capacities have a close relationship with Value‐at‐Risk (VaR) and Conditional Value‐at‐Risk (CVaR) risk measures. A Value of Stochastic Solutions is calculated to illustrate the benefits of the stochastic over the deterministic model approach.