Numerical solution of continuous-time DSGE modelsunder Poisson uncertainty

We propose a simple and powerful method for determining the transition processin continuous-time DSGE models under Poisson uncertainty numerically. The idea isto transform the system of stochastic dierential equations into a system of functionaldierential equations of the retarded type. We then use the Waveform Relaxationalgorithm to provide a guess of the policy function and solve the resulting system ofordinary dierential equations by standard methods and x-point iteration. Analyticalsolutions are provided as a benchmark from which our numerical method can be usedto explore broader classes of models...