Department of Economics and Business Economics

Olaf Posch

Numerical solution of continuous-time DSGE models under Poisson uncertainty

Research output: Working paperResearch


  • Wp10 08

    Final published version, 930 KB, PDF document

  • Olaf Posch
  • Timo Trimborn, Universiiy of Hannover, Germany
  • School of Economics and Management
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 differential equations into a system of functional differential equations of the retarded type. We then use the Waveform Relaxation algorithm to provide a guess of the policy function and solve the resulting system of ordinary differential equations by standard methods and fix-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 find that, even for non-linear policy functions, the maximum (absolute) error is very small.
Original languageEnglish
Place of publicationAarhus
PublisherInstitut for Økonomi, Aarhus Universitet
Number of pages33
Publication statusPublished - 2010

    Research areas

  • Continuous-time DSGE, Optimal stochastic control, Waveform Relaxation

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