This paper proposes a novel finite-state Markov chain approximation method for Markov processes with continuous support. The method can be used for both uni- and multivariate processes, as well as non-stationary processes such as those with a life-cycle component. The method is based on minimizing the information loss between a misspecified approximating model and the true data generating process. In contrast to existing methods, we provide both an optimal grid and transition probability matrix. We provide guidance on how to select the optimal number of grid points. The method outperforms existing methods in several dimensions, including parsimoniousness. We compare the performance of our method to existing methods through the lens of an asset-pricing model, and a life-cycle consumption-savings model. We find the choice of the discretization method matters for the accuracy of the model solutions, the welfare costs of risk, and the amount of wealth inequality a life-cycle model can generate.