Analytical and Numerical Solution of a Poisson RBC model - Christoph Schlegel (Technische Universität Dresden, Fakultät Wirtschaftswissenschaften, 2004)
This paper analyses a RBC model in continuous time featuring deterministic incremental development of technology and stochastic fundamental inventions arriving according to a Poisson process. Other than in standard RBC models, shocks are uncorrelated, irregular and rather seldom. In two special cases analytical solutions are presented. In the general case a delay differential equation (DDE) has to be solved. Standard numerical solution methods fail, because the steady state is path dependent. A new solution based on a modified method of steps for DDEs provides not only approximations but also upper and lower bounds for optimal consumption path and steady state.
Keywords: E32; O41; C61; C65; C68; 330; Business cycle models with poisson shocks; RBC models in continuous time; Delay differential equations; Real Business Cycle; Schock; Stochastischer Prozess; Theorie