Abstract
This note discusses a stochastic optimal growth model in which the optimal paths can be obtained by a simple direct argument. The structural characteristics of the model are the infinite horizon, the form of the instantaneous utility function, and uncertainty as a Wiener process in a linear production constraint. The note explains that, for optimality, at each point in time a formally identical problem must be solved. This implies that the optimal saving ratio must be constant.
A proof, employing the rules of stochastic calculus, that the ensuing paths are the unique globally optimal paths is also given.
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References
Arnold, L. (1974):Stochastic Differential Equations: Theory and Applications. New York: John Wiley & Sons.
Bismut, J.-M. (1975): “Growth and Optimal Intertemporal Allocation of Risks.”Journal of Economic Theory 10: 239–257.
Cass, D. (1965): “Optimum Growth in an Aggregative Model of Capital Accumulation.”Review of Economic Studies 32: 233–240.
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We are very grateful to two referees of this journal for their invaluable comments and suggestions.
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Glycopantis, D., Muir, A. On the solution of a stochastic optimal growth model. Zeitschr. f. Nationalökonomie 54, 125–142 (1991). https://doi.org/10.1007/BF01227081
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DOI: https://doi.org/10.1007/BF01227081