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Numerical solution of continuous-time DSGE models under Poisson uncertainty

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Author Info

  • Olaf Posch

    ()
    (Aarhus University, Denmark)

  • Timo Trimborn

    (University of Hannover)

Abstract

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.

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Bibliographic Info

Paper provided by School of Economics and Management, University of Aarhus in its series Economics Working Papers with number 2010-08.

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Length: 33
Date of creation: 10 Jun 2010
Date of revision:
Handle: RePEc:aah:aarhec:2010-08

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Web page: http://www.econ.au.dk/afn/

Related research

Keywords: Continuous-time DSGE; Optimal stochastic control; Waveform Relaxation;

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Cited by:
  1. Poudel, Diwakar & Sandal, Leif K. & Steinshamn, Stein I. & Kvamsdal, Sturla F., 2012. "Do Species Interactions and Stochasticity Matter to Optimal Management of Multispecies Fisheries?," Discussion Papers 2012/1, Department of Business and Management Science, Norwegian School of Economics.
  2. Poudel, Diwakar & Sandal, Leif K., 2014. "Stochastic Optimization for Multispecies Fisheries in the Barents Sea," Discussion Papers 2014/2, Department of Business and Management Science, Norwegian School of Economics.

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