A nonlinear stochastic growth model on discrete time domains

Abstract

In this paper, we introduce nonlinear stochastic dynamic problems on discrete time domains where events may occur at unevenly spaced time points. We define Euler equation and transversality condition for the problem. We prove that the Euler equation and the transversality condition are sufficient for the existence of the optimal solution. Next we generalize discrete time Cagan type rational expectation model to multivariate case. As an application of the main results, we obtain an explicit solution to a log-linearized nonlinear stochastic growth model.

Keywords:

• Optimization
• stochastic dynamic programming
• rational expectations

AMS Subject Classifications:

• 39A10
• 49J05
• 49J15
• 34N05

Acknowledgements

We thank the referees for their careful review and constructive comments on the manuscript.

Notes

No potential conflict of interest was reported by the authors.