Sustainability in the Stochastic Ramsey Model
Rabi Bhattacharya, Hyeonju Kim, Mukul Majumdar

TL;DR
This paper examines the probability of maintaining constant consumption in a stochastic Ramsey model with random output-capital ratios, introducing Chebyshev inequality-based estimates and numerical analyses.
Contribution
It provides new probabilistic estimation methods for sustaining consumption in stochastic Ramsey models, expanding on existing results with Chebyshev inequalities and numerical calculations.
Findings
Chebyshev inequalities can estimate sustainability probabilities
Numerical results illustrate the effectiveness of the estimates
Probabilistic analysis enhances understanding of stochastic consumption sustainability
Abstract
In this paper we provide a self-contained exposition of the problem of sustaining a constant consumption level in a Ramsey model. Our focus is on the case in which the output capital-ratio is random. After a brief review of the known results on the probabilities of sustaining a target consumption from an initial stock, we present some new results on estimating the probabilities by using Chebyshev inequalities. Some numerical calculations for these estimates are also provided.
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