This paper presents an alternative method for the stochastic simulation of nonlinear and possibly non-differentiable models with large state spaces. We compare our method to other existing methods, and show that the accuracy is satisfactory. We then use the method to analyze the features of an intertemporal optimizing consumption-saving model, when the utility function is time non-separable and when liquidity constraints are imposed. Two non-separabilities are studied, habit persistence and durability of the commodity. As the model has no closed-form solution, we compute deterministic and stochastic solution paths. It enables us to compare income and consumption volatility, and to describe the density of consumption under the different hypotheses on the utility function.