Numerical solution of continuous-time DSGE models under Poisson uncertainty Olaf Posch(a) and Timo Trimborn(b)

We propose a simple and powerful method for determining the transition process in continuous-time DSGE models under Poisson uncertainty numerically. The idea is to transform the system of stochastic dierential equations into a system of functional dierential equations of the retarded type. We use the Waveform Relaxation algorithm to provide a guess of the policy function and solve the resulting system of ordinary dierential equations by standard methods and x-point iteration. Analytical solutions are provided as a benchmark from which our numerical method can be used to explore broader classes of models. We illustrate the algorithm simulating both the stochastic neoclassical growth model and the Lucas model under Poisson uncertainty which is motivated by the Barro-Rietz rare disaster hypothesis. We nd that, even for non-linear policy functions, the maximum (absolute) error is very small