Dynamic stochastic general equilibrium models with ex-post heterogeneity due to idiosyncratic risk pose numerous challenges stemming from the cross-sectional distribution of endogenous variables which changes stochastically over time due to aggregate risk. In this thesis, I tackle various open questions. My first contribution is of a theoretical nature as I establish existence and uniqueness of the Aiyagari-Bewley growth model. The second challenge I address has a more practical concern. I propose a new numerical method to compute solutions to heterogeneous agent models. With the derived approximation error bounds, I ensure convergence to the rational expectations equilibrium. Equipped with this novel theoretically founded method, I show that even two standard economic models like the Aiyagari-Bewley growth model and the Huggett economy yield intriguing results. When agents progressively share idiosyncratic risk, heterogeneity increasingly amplifies aggregate risk. Furthermore, the volatility of the expected stationary cross-sectional distribution and of the stationary price distribution rises.