Exact Present Solution with Consistent Future Approximation: A Gridless Algorith to Solve Stochastic Dynamic Models

This paper proposes an algorithm that finds model solutions at a particular point in the state space by solving a simple system of equations. The key step is to characterize future behavior with a Taylor series expansion of the current period's behavior around the contemporaneous values for the state variables. Since current decisions are solved from the original model equations, the solution incorporates nonlinearities and uncertainty. The algorithm is used to solve the model considered in Coeurdacier, Rey, and Winant (2011), which is a challenging model because it has no steady state and uncertainty is necessary to keep the model well behaved. We show that our algorithm can generate accurate solutions even when the model series are quite volatile. The solution generated by the risky-steady-state algorithm proposed in Coeurdacier, Rey, and Winant (2011), in contrast, is shown to be not accurate.