In this paper we prove the existence of recursive equilibria in stochastic production economies with infinitely lived agents and incomplete financial markets. We consider a general dynamic model with several commodities, which encompasses heterogeneous agent versions of both the Lucas asset pricing model and the stochastic neo-classical growth model as special cases. Our main assumption is that there are atomless shocks to fundamentals that have a purely transitory component and a component that does not depend on last period's shocks directly.

We present a flexible and scalable method for computing global solutions of highdimensional stochastic dynamic models.Within a time iteration or value function iteration setup, we interpolate functions using an adaptive sparse grid algorithm.With increasing dimensions, sparse grids grow much more slowly than standard tensor product grids.Moreover, adaptivity adds a second layer of sparsity, as grid points are added only where they are most needed, for instance, in regions with steep gradients or at nondifferentiabilities.To further speed up the solution process, our implementation is fully hybrid parallel, combining distributed and shared memory parallelization paradigms, and thus permits an efficient use of high-performance computing architectures.To demonstrate the broad applicability of our method, we solve two very different types of dynamic models: first, high-dimensional international real business cycle models with capital adjustment costs and irreversible investment; second, multiproduct menu-cost models with temporary sales and economies of scope in price setting.