DMCA
Dynamic programming methods for Optimal Con- trol of PDE’s arising in Economics
BibTeX
@MISC{Fabbri_dynamicprogramming,
author = {Giorgio Fabbri and Silvia Faggian and Fausto Gozzi},
title = {Dynamic programming methods for Optimal Con- trol of PDE’s arising in Economics},
year = {}
}
Share
 |
 |
 |
 |
||
OpenURL
Abstract
We consider the following economic problem: modelling the vintage capital structure of an economic system. The problem is naturally for-mulated as an optimal control problem where the state equation is either a first order PDE or a delay equation. The optimal state-control couple describe the behavior of the economic agent. We formulate the problem as the optimal control of an ODE’s in a Hilbert space using standard tech-niques of semigroup theory and we develop the dynamic programming approach for this problem. The HJB equation cannot be studied with the existing techniques due the special features of the problem (the semi-group appearing in the state equation is not analytic, boundary control terms appear, the cost is not smooth). We show some new results on this equation and we apply them to find an optimal feedback for the economic problem 1
Keyphrases
optimal con trol state equation optimal control new result economic system economic problem optimal feedback first order pde optimal state-control couple hjb equation cannot optimal control problem vintage capital structure hilbert space standard tech-niques boundary control term delay equation dynamic programming approach semigroup theory following economic problem special feature economic agent
