Using dynamic programming with adaptive grid scheme for optimal control problems in economics

L. Grüne, W. Semmler: Using dynamic programming with adaptive grid scheme for optimal control problems in economics
Journal of Economic Dynamics and Control 28 (12), 2427 - 2456, 2004

Smart-Link: http://www.elsevier.com/locate/jedc
DOI: 10.1016/j.jedc.2003.11.002
Keywords: dynamic optimization; dynamic programming; adaptive grid scheme
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Abstract:

The study of the solutions of dynamic models with optimizing agents have often been limited by a lack of available analytical techniques to explicitly find the global solution paths. On the other hand the application of numerical techniques such as dynamic programming (DP) to find the solution in interesting regions of the state state was restricted by the use of fixed grid size techniques. Following Grüne (1997) in this paper an adaptive grid scheme is used for finding the global solutions of discrete time Hamilton-Jacobi-Bellman (HJB) equations. Local error estimates are established and an adapting iteration for the discretization of the state space is developed. The advantage of the use of adaptive grid scheme is demonstrated by computing the solution paths of one and two dimensional economic models which exhibit complicated dynamics due to multiple equilibria, thresholds (Skiba sets) separating domains of attraction and periodic solutions. The studied examples are from economic growth, investment theory, environmental and resource economics.

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