A Stochastic Version of the Ramsey’s Growth Model

Gabriel Zacarías-Espinoza, Hugo Cruz-Suárez, Enrique Lemus-Rodríguez

Abstract

In this paper we study a version of Ramsey’s discrete time Growth Model where the evolution of Labor through time is stochastic. Taking advantage of recent theoretical results in the field of Markov Decision Processes, a first set of conditions on the model are established that guarantee a long-term stable behavior of the underlying Markov chain.

References

  1. Brida, J. G., Cayssials, G., and Pereyra, J. S. (2015). The discrete Ramsey model with decreasing population growth rate. Dyn. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms, 22(2):97-115.
  2. Cruz-Suárez, H. and Montes-de Oca, R. (2008). An envelope theorem and some applications to discounted Markov decision processes. Math. Methods Oper. Res., 67(2):299-321.
  3. Cruz-Suárez, H., Montes-de Oca, R., and Zacarías, G. (2011). A consumption-investment problem modelled as a discounted Markov decision process. Kybernetika (Prague), 47(6):909-929.
  4. Cruz-Suárez, H., Zacarías-Espinoza, G., and V ázquezGuevara, V. (2012). A version of the Euler equation in discounted Markov decision processes. J. Appl. Math., pages Art. ID 103698, 16.
  5. Ekeland, I. (2010). From Frank Ramsey to René Thom: a classical problem in the calculus of variations leading to an implicit differential equation. Discrete Contin. Dyn. Syst., 28(3):1101-1119.
  6. Hernández-Lerma, O. and Lasserre, J. B. (1996). Discretetime Markov control processes, volume 30 of Applications of Mathematics (New York). Springer-Verlag, New York. Basic optimality criteria.
  7. Jaskiewicz, A. and Nowak, A. S. (2011). Discounted dynamic programming with unbounded returns: application to economic models. J. Math. Anal. Appl., 378(2):450-462.
  8. Kamihigashi, T. (2006). Almost sure convergence to zero in stochastic growth models. Economic Theory, 29(1):231-237.
  9. Le Van, C. and Dana, R.-A. (2003). Dynamic programming in economics, volume 5 of Dynamic Modeling and Econometrics in Economics and Finance. Kluwer Academic Publishers, Dordrecht.
  10. Meyn, S. and Tweedie, R. L. (2009). Markov chains and stochastic stability. Cambridge University Press, Cambridge, second edition. With a prologue by Peter W. Glynn.
  11. Nishimura, K. and Stachurski, J. (2005). Stability of stochastic optimal growth models: a new approach. J. Econom. Theory, 122(1):100-118.
  12. Peligrad, M. and Gut, A. (1999). Almost-sure results for a class of dependent random variables. J. Theoret. Probab., 12(1):87-104.
  13. Ramsey, F. (1928). A matemathical theory of saving. Econ. J., 38:543-559.
  14. SladkÉ, K. (2012). Some remarks on stochastic version of the ramsey growth model. Bulletin of the Czech Econometric Society., 19:139-152.
  15. Stachurski, J. (2009). Economic dynamics. MIT Press, Cambridge, MA. Theory and computation.
Download


Paper Citation


in Harvard Style

Zacarías-Espinoza G., Cruz-Suárez H. and Lemus-Rodríguez E. (2016). A Stochastic Version of the Ramsey’s Growth Model . In Proceedings of 5th the International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES, ISBN 978-989-758-171-7, pages 323-329. DOI: 10.5220/0005752503230329


in Bibtex Style

@conference{icores16,
author={Gabriel Zacarías-Espinoza and Hugo Cruz-Suárez and Enrique Lemus-Rodríguez},
title={A Stochastic Version of the Ramsey’s Growth Model},
booktitle={Proceedings of 5th the International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},
year={2016},
pages={323-329},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005752503230329},
isbn={978-989-758-171-7},
}


in EndNote Style

TY - CONF
JO - Proceedings of 5th the International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,
TI - A Stochastic Version of the Ramsey’s Growth Model
SN - 978-989-758-171-7
AU - Zacarías-Espinoza G.
AU - Cruz-Suárez H.
AU - Lemus-Rodríguez E.
PY - 2016
SP - 323
EP - 329
DO - 10.5220/0005752503230329