Ramsey Stochastic Model via Multistage Stochastic Programming

Ramsey model belongs to “classical” economic dynamic models. It has been (1928) originally constructed (with a farmer’s interpretation) in a deterministic discrete setting. To solve it Lagrangean or dynamic programming techniques can be employed. Later, this model has been generalized to a stochastic version. Time horizon in the original deterministic model as well as in modified stochastic one can be considered finite or infinite. We plan to deal with the stochastic model and finite horizon. However, in spite of the classical approach to analyze it we employ a stochastic programming technique. This approach gives a possibility to employ well known results on stability and empirical estimates also in the case of the Ramsey model. However, first we introduce some confidence intervals. To obtain the new assertions we restrict our consideration mostly to the case when the “underlying” random element follows autoregressive (or at least Markov) sequence.