We examine techniques for the analytical and numerical solution of state-dependent differential-difference equations. Such equations occur in the continuous-time modelling of vintage capital growth models, which form an important class of models in modem economic growth theory. The theoretical treat
Numerical solution by iterative methods of a class of vintage capital models
β Scribed by Raouf Boucekkine; Marc Germain; Omar Licandro; Alphonse Magnus
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 156 KB
- Volume
- 25
- Category
- Article
- ISSN
- 0165-1889
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β¦ Synopsis
We build up an iterative numerical procedure in order to solve vintage capital growth models with nonlinear utility functions and Leontie! technologies, a class of models intensively used in the literature since the early 1990s. The numerical procedure is of the relaxation type and uses a step-by-step maximization scheme for updating. The procedure is close to the cyclic coordinate descent algorithm as described in the computational mathematics literature. We explain why and how our numerical scheme is suitable to handle the considered class of models.
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Recently, numerical solutions of stochastic differential equations have received a great deal of attention. Numerical approximation schemes are invaluable tools for exploring their properties. In this paper, we introduce a class of stochastic age-dependent (vintage) capital system with Poisson jumps