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EnglishWe deal with an infinite horizon, infinite dimensional stochastic optimal control problem arising in the study of economic growth in time-space. Such a problem has been the object of various papers in deterministic cases when the possible presence of stochastic disturbances is ignored (see, e.g., [P. Brito, The Dynamics of Growth and Distribution in a Spatially Heterogeneous World, working paper 2004/14, ISEG-Lisbon School of Economics and Management, University of Lisbon, 2004], [R. Boucekkine, C. Camacho, and G. Fabbri, J. Econom. Theory, 148 (2013), pp. 2719--2736], [G. Fabbri, J. Econom. Theory, 162 (2016), pp. 114--136], and [R. Boucekkine, G. Fabbri, S. Federico, and F. Gozzi, J. Econom. Geography, 19 (2019), pp. 1287--1318]). Here we propose and solve a stochastic generalization of such models where the stochastic term, in line with the standard stochastic economic growth models (see, e.g., the books [A. G. Malliaris and W. A. Brock, Stochastic Methods in Economics and Finance, Advanced Textbooks in Economics 17, North Holland, 1982, Chapter 3] and [H. Morimoto, Stochastic Control and Mathematical Modeling: Applications in Economics, Cambridge Books, 2010, Chapter 9]), is a multiplicative one, driven by a cylindrical Wiener process. The problem is studied using the dynamic programming approach. We find an explicit solution of the associated HJB equation, use a verification type result to prove that such a solution is the value function, and find the optimal feedback strategies. Finally, we use this result to study the asymptotic behavior of the optimal trajectories.
A Stochastic Model of Economic Growth in Time-Space / Gozzi, Fausto; Leocata, Marta. - In: SIAM JOURNAL ON CONTROL AND OPTIMIZATION. - ISSN 0363-0129. - 60:2(2022), pp. 620-651. [10.1137/21M1414206]
| Titolo: | A Stochastic Model of Economic Growth in Time-Space | |
| Autori: | ||
| Data di pubblicazione: | 2022 | |
| Rivista: | ||
| Citazione: | A Stochastic Model of Economic Growth in Time-Space / Gozzi, Fausto; Leocata, Marta. - In: SIAM JOURNAL ON CONTROL AND OPTIMIZATION. - ISSN 0363-0129. - 60:2(2022), pp. 620-651. [10.1137/21M1414206] | |
| Handle: | http://hdl.handle.net/11385/217655 | |
| Appare nelle tipologie: | 01.1 - Articolo su rivista (Article) |
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