[en] We solve a bimodal optimal control problem with a non-concavity and uncertainty through a Poisson process underlying the transition from a mode to another. We use a dynamic programming approach and are able to uncover the global optimal dynamics (including optimal
non-monotonic paths) under a few linear-quadratic assumption, which do not get rid of the non-concavity of the problem. This is in contrast to the related literature on pollution control under irreversibility which usually explores local dynamics along monotonic solution paths to first order
Pontryagin conditions.
Disciplines :
Mathématiques
Auteur, co-auteur :
Boucekkine, Raouf
Ruan, Weihua
ZOU, Benteng ; University of Luxembourg > Faculty of Law, Economics and Finance (FDEF) > Department of Economics and Management (DEM)
Co-auteurs externes :
yes
Langue du document :
Anglais
Titre :
A dynamic programming approach to optimal pollution control under uncertain irreversibility: The Poisson case
R. Boucekkine, A. Pommeret, F. Prieur, Technological vs. ecological switch and the Environmental Kuznets Curve, American Journal of Agricultural Economics, 95 (2013) 252-260.
M.H.A. Davis, Piecewise-deterministic Markov processes: a general class of non-diffusion stochastic models, Journal of the Royal Statistical Society (B), 46 (1984) 353-388.
E. J. Dockner, S. Jφ rgensen, N. V. Long, G. Sorger, Differential Games in Economics and Management Science, Cambridge, Cambridge University Press, 2000.
M. Farid, Optimal control, piecewise-deterministic processes and viscosity solutions, Ph.D. Thesis, University of London, 1997.
C. Holling, Resilience and stability of ecological systems, Review of Ecology and Systematics 4 (1973) 1-23.
S.M. Lenhar, N. Yamada, Viscosity solutions assciated with switching game for piecewise-deterministic processes, Stochastics and Stochastics Reports 38 (1992) 27-47.
A. Le Kama, A. Pommeret, F. Prieur, Optimal emission policy under the risk of irreversible pollution, Journal of Public Economic Theory, 16 (2014) 959-980.
O. Tahvonen, C. Withagen, Optimality of irreversible pollution accumulation, Journal of Economic Dynamics and Control, 20 (1996) 1775-1795.
Y. Tsur, A. Zemel, Uncertainty and irreversibility in groundwater resource management, Journal of Environmental Economics and Management, 29 (1995) 149-161.
D. Vermes, Optimal control of piecewise-deterministic Markov processes, Stochastics, 14 (1985) 165-208.
