Simplifying numerical analyses of Hamilton-Jacobi-Bellman equations

Dirk Bethmann, Markus Reiß

Research output: Contribution to journalArticle

2 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)101-128
Number of pages28
JournalJournal of Economics/ Zeitschrift fur Nationalokonomie
Volume107
Issue number2
DOIs
Publication statusPublished - 2012 Oct 1
Externally publishedYes

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Optimization problem
Hamilton-Jacobi-Bellman equation
Value function
Endogenous growth model
Optimal control
Differential equations
Representative agent
Transitional dynamics

Keywords

  • Initial value problem
  • Symmetric equilibrium
  • Transitional dynamics
  • U-shaped growth rates
  • Value function approach

ASJC Scopus subject areas

  • Economics and Econometrics
  • Business, Management and Accounting(all)

Cite this

Simplifying numerical analyses of Hamilton-Jacobi-Bellman equations. / Bethmann, Dirk; Reiß, Markus.

In: Journal of Economics/ Zeitschrift fur Nationalokonomie, Vol. 107, No. 2, 01.10.2012, p. 101-128.

Research output: Contribution to journalArticle

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