We introduce and deploy a generic, highly scalable computational method to solve high-dimensional dynamic stochastic economic models on high-performance computing platforms. Within an MPI---TBB parallel, nonlinear time iteration framework, we approximate economic policy functions using an adaptive sparse grid algorithm with d-linear basis functions that is combined with a dimensional decomposition scheme. Numerical experiments on "Piz Daint" (Cray XC30) at the Swiss National Supercomputing Centre show that our framework scales nicely to at least 1,000 compute nodes. As an economic application, we compute global solutions to international real business cycle models up to 200 continuous dimensions with significant speedup values over state-of-the-art techniques.