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arXiv · 2203.10595

On the Fragility of the Basis on the Hamilton-Jacobi-Bellman Equation in Economic Dynamics

Yuhki Hosoya
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Abstract

In this paper, we provide an example of the optimal growth model in which there exist infinitely many solutions to the Hamilton-Jacobi-Bellman equation but the value function does not satisfy this equation. We consider the cause of this phenomenon, and find that the lack of a solution to the original problem is crucial. We show that under several conditions, there exists a solution to the original problem if and only if the value function solves the Hamilton-Jacobi-Bellman equation. Moreover, in this case, the value function is the unique nondecreasing concave solution to the Hamilton-Jacobi-Bellman equation. We also show that without our conditions, this uniqueness result does not hold.

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Yuhki Hosoya. 2022-03-20. On the Fragility of the Basis on the Hamilton-Jacobi-Bellman Equation in Economic Dynamics. https://doi.org/10.1016/j.jmateco.2024.102940

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