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Simplifying numerical analyses of Hamilton-Jacobi-Bellman equations

Dirk Bethmann and Markus Reiß
Journal of Economics
Vol. 107, No. 2 (October 2012), pp. 101-128
Published by: Springer
Stable URL: http://www.jstor.org/stable/43574609
Page Count: 28
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Simplifying numerical analyses of Hamilton-Jacobi-Bellman equations
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Abstract

We introduce a simple method for computing value functions. The method is demonstrated by solving for transitional dynamics in the Uzawa and Lucas endogenous growth model. We use the value function approach to solve both the social planner's optimization problem in the centralized economy and the representative agent's optimization problem in the decentralized economy. The complexity of the Hamilton-Jacobi-Bellman equations is significantly reduced to an initial value problem for one ordinary differential equation. This approach allows us to find the optimal controls for the non-concave Hamiltonian in the centralized case and to identify the symmetric equilibrium in the decentralized case.

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